chapter 1 resource masters - math problem solving · ©glencoe/mcgraw-hill v glencoe geometry...
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Chapter 1Resource Masters
Geometry
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks.
Study Guide and Intervention Workbook 0-07-860191-6Skills Practice Workbook 0-07-860192-4Practice Workbook 0-07-860193-2Reading to Learn Mathematics Workbook 0-07-861061-3
ANSWERS FOR WORKBOOKS The answers for Chapter 1 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Geometry. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 0-07-846589-3 GeometryChapter 1 Resource Masters
1 2 3 4 5 6 7 8 9 10 009 11 10 09 08 07 06 05 04 03
© Glencoe/McGraw-Hill iii Glencoe Geometry
Contents
Vocabulary Builder . . . . . . . . . . . . . . . . vii
Lesson 1-1Study Guide and Intervention . . . . . . . . . . . 1–2Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 3Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Reading to Learn Mathematics . . . . . . . . . . . . 5Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Lesson 1-2Study Guide and Intervention . . . . . . . . . . . 7–8Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 9Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Reading to Learn Mathematics . . . . . . . . . . . 11Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Lesson 1-3Study Guide and Intervention . . . . . . . . . 13–14Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 15Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Reading to Learn Mathematics . . . . . . . . . . . 17Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Lesson 1-4Study Guide and Intervention . . . . . . . . . 19–20Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 21Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Reading to Learn Mathematics . . . . . . . . . . . 23Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Lesson 1-5Study Guide and Intervention . . . . . . . . . 25–26Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 27Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Reading to Learn Mathematics . . . . . . . . . . . 29Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Lesson 1-6Study Guide and Intervention . . . . . . . . . 31–32Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 33Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Reading to Learn Mathematics . . . . . . . . . . . 35Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Chapter 1 AssessmentChapter 1 Test, Form 1 . . . . . . . . . . . . . . 37–38Chapter 1 Test, Form 2A . . . . . . . . . . . . . 39–40Chapter 1 Test, Form 2B . . . . . . . . . . . . . 41–42Chapter 1 Test, Form 2C . . . . . . . . . . . . . 43–44Chapter 1 Test, Form 2D . . . . . . . . . . . . . 45–46Chapter 1 Test, Form 3 . . . . . . . . . . . . . . 47–48Chapter 1 Open-Ended Assessment . . . . . . . 49Chapter 1 Vocabulary Test/Review . . . . . . . . 50Chapter 1 Quizzes 1 & 2 . . . . . . . . . . . . . . . . 51Chapter 1 Quizzes 3 & 4 . . . . . . . . . . . . . . . . 52Chapter 1 Mid-Chapter Test . . . . . . . . . . . . . 53Chapter 1 Cumulative Review . . . . . . . . . . . . 54Chapter 1 Standardized Test Practice . . . 55–56
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A29
© Glencoe/McGraw-Hill iv Glencoe Geometry
Teacher’s Guide to Using theChapter 1 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 1 Resource Masters includes the core materials neededfor Chapter 1. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theGeometry TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 1-1.Encourage them to add these pages to theirGeometry Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Geometry addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Geometry
Assessment OptionsThe assessment masters in the Chapter 1Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Geometry. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of geometry conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and short-responsequestions. Bubble-in and grid-in answersections are provided on the master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 58–59. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
11
© Glencoe/McGraw-Hill vii Glencoe Geometry
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 1.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Geometry Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
acute angle
adjacent angles
uh·JAY·suhnt
angle
angle bisector
collinear
koh·LIN·ee·uhr
complementary angles
congruent
kuhn·GROO·uhnt
coplanar
koh·PLAY·nuhr
line segment
linear pair
(continued on the next page)
© Glencoe/McGraw-Hill viii Glencoe Geometry
Vocabulary Term Found on Page Definition/Description/Example
midpoint
obtuse angle
perimeter
perpendicular lines
polygon
PAHL·ee·gahn
ray
right angle
segment bisector
supplementary angles
vertical angles
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
11
Study Guide and InterventionPoints, Lines, and Planes
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
© Glencoe/McGraw-Hill 1 Glencoe Geometry
Less
on
1-1
Name Points, Lines, and Planes In geometry, a point is a location, a line containspoints, and a plane is a flat surface that contains points and lines. If points are on the sameline, they are collinear. If points on are the same plane, they are coplanar.
Use the figure to name each of the following.
a. a line containing point A
The line can be named as �. Also, any two of the three points on the line can be used to name it.
AB���, AC���, or BC���
b. a plane containing point D
The plane can be named as plane N or can be named using three noncollinear points in the plane, such as plane ABD, plane ACD, and so on.
Refer to the figure.
1. Name a line that contains point A.
2. What is another name for line m ?
3. Name a point not on AC���.
4. Name the intersection of AC��� and DB���.
5. Name a point not on line � or line m .
Draw and label a plane Q for each relationship.
6. AB��� is in plane Q.
7. ST��� intersects AB��� at P.
8. Point X is collinear with points A and P.
9. Point Y is not collinear with points T and P.
10. Line � contains points X and Y.
�Q
AB
S
P
TY
X
�
Pm
AB
EC
D
�
N
AB
C
DExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 2 Glencoe Geometry
Points, Lines, and Planes in Space Space is a boundless, three-dimensional set ofall points. It contains lines and planes.
a. How many planes appear in the figure?
There are three planes: plane N , plane O, and plane P.
b. Are points A, B, and D coplanar?
Yes. They are contained in plane O.
Refer to the figure.
1. Name a line that is not contained in plane N.
2. Name a plane that contains point B.
3. Name three collinear points.
Refer to the figure.
4. How many planes are shown in the figure?
5. Are points B, E, G, and H coplanar? Explain.
6. Name a point coplanar with D, C, and E.
Draw and label a figure for each relationship.
7. Planes M andN intersect in HJ���.
8. Line r is in plane N , line s is in plane M, and lines r and sintersect at point J.
9. Line t contains point H and line t does not lie in plane M orplane N.
N
Ms
t
r
HJ
A B
CD
EF
G HI
J
N
A
C
B
D
E
NO
P
AB
CD
Study Guide and Intervention (continued)
Points, Lines, and Planes
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
ExampleExample
ExercisesExercises
Skills PracticePoints, Lines, and Planes
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
© Glencoe/McGraw-Hill 3 Glencoe Geometry
Less
on
1-1
Refer to the figure.
1. Name a line that contains point D.
2. Name a point contained in line n.
3. What is another name for line p?
4. Name the plane containing lines n and p.
Draw and label a figure for each relationship.
5. Point K lies on RT���. 6. Plane J contains line s.
7. YP��� lies in plane B and contains 8. Lines q and f intersect at point Zpoint C, but does not contain point H. in plane U.
Refer to the figure.
9. How many planes are shown in the figure?
10. How many of the planes contain points F and E?
11. Name four points that are coplanar.
12. Are points A, B, and C coplanar? Explain.
WA
B
E
C
DF
U
q f
Z
HP
B
CY
J
sTR
K
G
n
A BD
C
p
© Glencoe/McGraw-Hill 4 Glencoe Geometry
Refer to the figure.
1. Name a line that contains points T and P.
2. Name a line that intersects the plane containing points Q, N, and P.
3. Name the plane that contains TN��� and QR���.
Draw and label a figure for each relationship.
4. AK��� and CG��� intersect at point M 5. A line contains L(�4, �4) and M(2, 3). Line in plane T. q is in the same coordinate plane but does
not intersect LM���. Line q contains point N.
Refer to the figure.
6. How many planes are shown in the figure?
7. Name three collinear points.
8. Are points N, R, S, and W coplanar? Explain.
VISUALIZATION Name the geometric term(s) modeled by each object.
9. 10. 11.
12. a car antenna 13. a library card
strings
tip of pinSTOP
A M N
PW S
X R
QT
L
M
N
q
x
y
O
KT
M
C
GA
S
j
g
hT
M
N
Q
R
P
Practice Points, Lines, and Planes
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
Reading to Learn MathematicsPoints, Lines, and Planes
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
© Glencoe/McGraw-Hill 5 Glencoe Geometry
Less
on
1-1
Pre-Activity Why do chairs sometimes wobble?
Read the introduction to Lesson 1-1 at the top of page 6 in your textbook.
• Find three pencils of different lengths and hold them upright on yourdesk so that the three pencil points do not lie along a single line. Can youplace a flat sheet of paper or cardboard so that it touches all three pencilpoints?
• How many ways can you do this if you keep the pencil points in the sameposition?
• How will your answer change if there are four pencil points?
Reading the Lesson
1. Complete each sentence.
a. Points that lie on the same lie are called points.
b. Points that do not lie in the same plane are called points.
c. There is exactly one through any two points.
d. There is exactly one through any three noncollinear points.
2. Refer to the figure at the right. Indicate whether each statement is true or false.
a. Points A, B, and C are collinear.
b. The intersection of plane ABC and line m is point P.
c. Line � and line m do not intersect.
d. Points A, P,and B can be used to name plane U.
e. Line � lies in plane ACB.
3. Complete the figure at the right to show the following relationship: Lines �, m, and n are coplanar and lie in plane Q. Lines � and m intersect at point P. Line nintersects line m at R, but does not intersect line �.
Helping You Remember
4. Recall or look in a dictionary to find the meaning of the prefix co-. What does this prefixmean? How can it help you remember the meaning of collinear?
Qn
m
�P
R
U
m
�PC
D
B
A
© Glencoe/McGraw-Hill 6 Glencoe Geometry
Points and Lines on a MatrixA matrix is a rectangular array of rows and columns. Points andlines on a matrix are not defined in the same way as in Euclideangeometry. A point on a matrix is a dot, which can be small orlarge. A line on a matrix is a path of dots that “line up.” Betweentwo points on a line there may or may not be other points. Threeexamples of lines are shown at the upper right. The broad line canbe thought of as a single line or as two narrow lines side by side.
Dot-matrix printers for computers used dots to form characters.The dots are often called pixels. The matrix at the right showshow a dot-matrix printer might print the letter P.
Draw points on each matrix to create the given figures.
1. Draw two intersecting lines that have 2. Draw two lines that cross but have four points in common. no common points.
3. Make the number 0 (zero) so that it 4. Make the capital letter O so that itextends to the top and bottom sides extends to each side of the matrix.of the matrix.
5. Using separate grid paper, make dot designs for several other letters. Which were theeasiest and which were the most difficult?
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-11-1
Study Guide and InterventionLinear Measure and Precision
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
© Glencoe/McGraw-Hill 7 Glencoe Geometry
Less
on
1-2
Measure Line Segments A part of a line between two endpoints is called a linesegment. The lengths of M�N� and R�S� are written as MN and RS. When you measure asegment, the precision of the measurement is half of the smallest unit on the ruler.
Find the length of M�N�.
The long marks are centimeters, and theshorter marks are millimeters. The length of M�N� is 3.4 centimeters. The measurement is accurate to within 0.5 millimeter, so M�N� isbetween 3.35 centimeters and 3.45centimeters long.
1cm 2 3 4
M N
Find the length of R�S�.
The long marks are inches and the short marks are quarter inches. The length of R�S�is about 1�
34� inches. The measurement is
accurate to within one half of a quarter inch,
or �18� inch, so R�S� is between 1�
58� inches and
1�78� inches long.
1 2in.
R S
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find the length of each line segment or object.
1. 2.
3. 4.
Find the precision for each measurement.
5. 10 in. 6. 32 mm 7. 44 cm
8. 2 ft 9. 3.5 mm 10. 2�12� yd
1cm 2 31 2in.
1in.
S T
1cm 2 3
A B
© Glencoe/McGraw-Hill 8 Glencoe Geometry
Calculate Measures On PQ���, to say that point M is between points P and Q means P, Q, and M are collinear and PM � MQ � PQ.
On AC���, AB � BC � 3 cm. We can say that the segments arecongruent, or A�B� � B�C�. Slashes on the figure indicate whichsegments are congruent.
AB
C
QMP
Study Guide and Intervention (continued)
Linear Measure and Precision
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
Find EF.
Calculate EF by adding ED and DF.
ED � DF � EF1.2 � 1.9 � EF
3.1 � EF
Therefore, E�F� is 3.1 centimeters long.
E1.2 cm 1.9 cm
FD
Find x and AC.
B is between A and C.
AB � BC � ACx � 2x � 2x � 5
3x � 2x � 5x � 5
AC � 2x � 5 � 2(5) � 5 � 15
A x 2x CB
2x � 5
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find the measurement of each segment. Assume that the art is not drawn to scale.
1. R�T� 2. B�C�
3. X�Z� 4. W�X�
Find x and RS if S is between R and T.
5. RS � 5x, ST � 3x, and RT � 48. 6. RS � 2x, ST � 5x � 4, and RT � 32.
7. RS � 6x, ST �12, and RT � 72. 8. RS � 4x, R�S� � S�T�, and RT � 24.
Use the figures to determine whether each pair of segments is congruent.
9. A�B� and C�D� 10. X�Y� and Y�Z�X
Y Z
3x � 5 5x � 1
9x2
A D
CB
11 cm
11 cm
5 cm5 cm
W Y
6 cm
XX ZY
3–4 in.31–
2 in.
A C
6 in.
23–4 in. BR T
2.0 cm 2.5 cm
S
Skills PracticeLinear Measure and Precision
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
© Glencoe/McGraw-Hill 9 Glencoe Geometry
Less
on
1-2
Find the length of each line segment or object.
1. 2.
Find the precision for each measurement.
3. 40 feet 4. 12 centimeters 5. 9�12� inches
Find the measurement of each segment.
6. N�Q� 7. A�C� 8. G�H�
Find the value of the variable and YZ if Y is between X and Z.
9. XY � 5p, YZ � p, and XY � 25 10. XY � 12, YZ � 2g, and XZ � 28
11. XY � 4m, YZ � 3m, and XZ � 42 12. XY � 2c � 1, YZ � 6c, and XZ � 81
Use the figures to determine whether each pair of segments is congruent.
13. B�E�, C�D� 14. M�P�, N�P� 15. W�X�, W�Z�
Y Z
WX
9 ft
5 ft 5 ft
N
P
M 10 yd
12 yd
12 ydE D
CB
5 m
2 m
3 m 3 m
F 9.7 mm HG
15 mmA4.9 cm 5.2 cm
CBQ1in. 11–
4 in.
NP
1 2in.
1cm 2 3 54
© Glencoe/McGraw-Hill 10 Glencoe Geometry
Find the length of each line segment or object.
1. 2.
Find the precision for each measurement.
3. 120 meters 4. 7�14� inches 5. 30.0 millimeters
Find the measurement of each segment.
6. P�S� 7. A�D� 8. W�X�
Find the value of the variable and KL if K is between J and L.
9. JK � 6r, KL � 3r, and JL � 27 10. JK � 2s, KL � s � 2, and JL � 5s � 10
Use the figures to determine whether each pair of segments is congruent.
11. T�U�, S�W� 12. A�D�, B�C� 13. G�F�, F�E�
14. CARPENTRY Jorge used the figure at the right to make a pattern for a mosaic he plans to inlay on a tabletop. Name all of the congruent segments in the figure.
D
A
BF
E C
G H
EF
5x
6xD C
BA
12.9 in.
12.7 in.
W
T S
U
2 ft
2 ft
3 ft
3 ft
W 89.6 cm YX
100 cmA
11–4 in.23–
8 in.
DCP4.7 cm18.4 cm
SQ
1cm 2 3 541 2in.
E F
Practice Linear Measure and Precision
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
Reading to Learn MathematicsLinear Measure and Precision
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
© Glencoe/McGraw-Hill 11 Glencoe Geometry
Less
on
1-2
Pre-Activity Why are units of measure important?
Read the introduction to Lesson 1-2 at the top of page 13 in your textbook.
• The basic unit of length in the metric system is the meter. How manymeters are there in one kilometer?
• Do you think it would be easier to learn the relationships between thedifferent units of length in the customary system (used in the UnitedStates) or in the metric system? Explain your answer.
Reading the Lesson
1. Explain the difference between a line and a line segment and why one of these can bemeasured, while the other cannot.
2. What is the smallest length marked on a 12-inch ruler?What is the smallest length marked on a centimeter ruler?
3. Find the precision of each measurement.a. 15 cmb. 15.0 cm
4. Refer to the figure at the right. Which one of the following statements is true? Explain your answer.A�B� � C�D� A�B� � C�D�
5. Suppose that S is a point on V�W� and S is not the same point as V or W. Tell whethereach of the following statements is always, sometimes, or never true.a. VS � SWb. S is between V and W.c. VS � VW � SW
Helping You Remember
6. A good way to remember terms used in mathematics is to relate them to everyday wordsyou know. Give three words that are used outside of mathematics that can help youremember that there are 100 centimeters in a meter.
A
B
4.5 cm 4.5 cm
DC
© Glencoe/McGraw-Hill 12 Glencoe Geometry
Points Equidistant from SegmentsThe distance from a point to a segment is zero if the point is on the segment. Otherwise, it is the length of the shortest segment from the point to the segment.
A figure is a locus if it is the set of all points that satisfy
a set of conditions. The locus of all points that are �14� inch
from the segment AB is shown by two dashed segments with semicircles at both ends.
1. Suppose A, B, C, and D are four different points, and consider the locus of all points x units from A�B� and x units from C�D�. Use any unit you findconvenient. The locus can take different forms. Sketch at least threepossibilities. List some of the things that seem to affect the form of the locus.
2. Conduct your own investigation of the locus of pointsequidistant from two segments. Describe your results on aseparate sheet of paper.
A BC D
P Q
R S
A
B
C
D
X
Y
A B
C DX Y
A B
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-21-2
Study Guide and InterventionDistance and Midpoints
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
© Glencoe/McGraw-Hill 13 Glencoe Geometry
Less
on
1-3
Distance Between Two Points
Distance on a Number Line Distance in the Coordinate Plane
AB � |b � a | or |a � b |x
y
OC(1, –1)
A(–2, –1)
B(1, 3)
Pythagorean Theorem:
a2 � b2 � c2
Distance Formula:
d � �(x2 ��x1)2 �� (y2 �� y1)2�
A B
a b
Find AB.
AB � |(�4) � 2|� |� 6|� 6
�5 �4 �3 �2 �1 0 1 2 3
A B
Find the distance between A(�2, �1) and B(1, 3).
Example 1Example 1 Example 2Example 2
Pythagorean Theorem
(AB)2 � (AC)2 � (BC)2
(AB)2 � (3)2 � (4)2
(AB)2 � 25
AB � �25�� 5
Distance Formula
d � �(x2 ��x1)2 �� (y2 �� y1)2�AB � �(1 � (��2))2�� (3 �� (�1))�2�AB � �(3)2 �� (4)2�
� �25�� 5
Use the number line to find each measure.
1. BD 2. DG
3. AF 4. EF
5. BG 6. AG
7. BE 8. DE
Use the Pythagorean Theorem to find the distance between each pair of points.
9. A(0, 0), B(6, 8) 10. R(�2, 3), S(3, 15)
11. M(1, �2), N(9, 13) 12. E(�12, 2), F(�9, 6)
Use the Distance Formula to find the distance between each pair of points.
13. A(0, 0), B(15, 20) 14. O(�12, 0), P(�8, 3)
15. C(11, �12), D(6, 2) 16. E(�2, 10), F(�4, 3)
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
ExercisesExercises
© Glencoe/McGraw-Hill 14 Glencoe Geometry
Midpoint of a Segment
Midpoint on a If the coordinates of the endpoints of a segment are a and b,
Number Line then the coordinate of the midpoint of the segment is �a �2
b�.
Midpoint on a If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
Coordinate Plane then the coordinates of the midpoint of the segment are ��x1 �
2x2�, �
y1 �
2y2��.
Find the coordinate of the midpoint of P�Q�.
The coordinates of P and Q are �3 and 1.
If M is the midpoint of P�Q�, then the coordinate of M is ��32� 1� � �
�22� or �1.
M is the midpoint of P�Q� for P(�2, 4) and Q(4, 1). Find thecoordinates of M.
M � ��x1 �
2x2�, �
y1 �
2y2�� � ���2
2� 4�, �
4 �2
1�� or (1, 2.5)
Use the number line to find the coordinate of the midpoint of each segment.
1. C�E� 2. D�G�
3. A�F� 4. E�G�
5. A�B� 6. B�G�
7. B�D� 8. D�E�
Find the coordinates of the midpoint of a segment having the given endpoints.
9. A(0, 0), B(12, 8) 10. R(�12, 8), S(6, 12)
11. M(11, �2), N(�9, 13) 12. E(�2, 6), F(�9, 3)
13. S(10, �22), T(9, 10) 14. M(�11, 2), N(�19, 6)
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
–3 –2 –1 0 1 2
P Q
Study Guide and Intervention (continued)
Distance and Midpoints
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
Example 1Example 1
Example 2Example 2
ExercisesExercises
Skills PracticeDistance and Midpoints
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
© Glencoe/McGraw-Hill 15 Glencoe Geometry
Less
on
1-3
Use the number line to find each measure.
1. LN 2. JL
3. KN 4. MN
Use the Pythagorean Theorem to find the distance between each pair of points.
5. 6.
7. K(2, 3), F(4, 4) 8. C(�3, �1), Q(�2, 3)
Use the Distance Formula to find the distance between each pair of points.
9. Y(2, 0), P(2, 6) 10. W(�2, 2), R(5, 2)
11. A(�7, �3), B(5, 2) 12. C(�3, 1), Q(2, 6)
Use the number line to find the coordinate of the midpoint of each segment.
13. D�E� 14. B�C�
15. B�D� 16. A�D�
Find the coordinates of the midpoint of a segment having the given endpoints.
17. T(3, 1), U(5, 3) 18. J(�4, 2), F(5, �2)
Find the coordinates of the missing endpoint given that P is the midpoint of N�Q�.
19. N(2, 0), P(5, 2) 20. N(5, 4), P(6, 3) 21. Q(3, 9), P(�1, 5)
–6 –4 –2 0 2 4 6 8 10 12
A B C D E
x
y
O
D
S
x
y
O
F
G
–6 –4 –2 0 2 4 6 8 10
J K L M N
© Glencoe/McGraw-Hill 16 Glencoe Geometry
Use the number line to find each measure.
1. VW 2. TV
3. ST 4. SV
Use the Pythagorean Theorem to find the distance between each pair of points.
5. 6.
Use the Distance Formula to find the distance between each pair of points.
7. L(�7, 0), Y(5, 9) 8. U(1, 3), B(4, 6)
Use the number line to find the coordinate of the midpoint of each segment.
9. R�T� 10. Q�R�
11. S�T� 12. P�R�
Find the coordinates of the midpoint of a segment having the given endpoints.
13. K(�9, 3), H(5, 7) 14. W(�12, �7), T(�8, �4)
Find the coordinates of the missing endpoint given that E is the midpoint of D�F�.
15. F(5, 8), E(4, 3) 16. F(2, 9), E(�1, 6) 17. D(�3, �8), E(1, �2)
18. PERIMETER The coordinates of the vertices of a quadrilateral are R(�1, 3), S(3, 3),T(5, �1), and U(�2, �1). Find the perimeter of the quadrilateral. Round to the nearest tenth.
–6 –4–10 –8 –2 0 2 4 6
P Q R S T
x
y
O
E
S
x
y
OM
Z
–6 –4–10 –8 –2 0 2 4 6 8
S T U V W
Practice Distance and Midpoints
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
Reading to Learn MathematicsDistance and Midpoints
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
© Glencoe/McGraw-Hill 17 Glencoe Geometry
Less
on
1-3
Pre-Activity How can you find the distance between two points without a ruler?
Read the introduction to Lesson 1-3 at the top of page 21 in your textbook.
• Look at the triangle in the introduction to this lesson. What is the specialname for A�B� in this triangle?
• Find AB in this figure. Write your answer both as a radical and as adecimal number rounded to the nearest tenth.
Reading the Lesson
1. Match each formula or expression in the first column with one of the names in thesecond column.
a. d � �(x2 ��x1)2 �� ( y2 �� y1)2� i. Pythagorean Theorem
b. �a �
2b
� ii. Distance Formula in the Coordinate Plane
c. XY � |a � b| iii. Midpoint of a Segment in the Coordinate Plane
d. c2 � a2 � b2 iv. Distance Formula on a Number Line
e. ��x1 �
2x2
�, �y1 �
2y2
�� v. Midpoint of a Segment on a Number Line
2. Fill in the steps to calculate the distance between the points M(4, �3) and N(�2, 7).
Let (x1, y1) � (4, �3). Then (x2, y2) � ( , ).
d � �����( � )2 � ( � )2
MN � �����( � )2 � ( � )2
MN � ���( )2 � ( )2
MN � ����
MN � ��Find a decimal approximation for MN to the nearest hundredth.
Helping You Remember
3. A good way to remember a new formula in mathematics is to relate it to one you alreadyknow. If you forget the Distance Formula, how can you use the Pythagorean Theorem tofind the distance d between two points on a coordinate plane?
© Glencoe/McGraw-Hill 18 Glencoe Geometry
Lengths on a GridEvenly-spaced horizontal and vertical lines form a grid.
You can easily find segment lengths on a grid if the endpoints are grid-lineintersections. For horizontal or verticalsegments, simply count squares. For diagonal segments, use the PythagoreanTheorem (proven in Chapter 7). This theorem states that in any right triangle,if the length of the longest side (the sideopposite the right angle) is c and the twoshorter sides have lengths a and b, then c2 � a2 � b2.
Find the measure of E�F� on the grid at the right. Locate a right triangle with E�F� as its longest side.
EF � �22 � 5�2� � �29� � 5.4 units
Find each measure to the nearest tenth of a unit.
1. I�J� 2. M�N� 3. R�S� 4. Q�S�
5. I�K� 6. J�K� 7. L�M� 8. L�N�
Use the grid above. Find the perimeter of each triangle to the nearest tenth of a unit.
9. � ABC 10. �QRS 11. � DEF 12. � LMN
13. Of all the segments shown on the 14. On the grid, 1 unit � 0.5 cm. How can the grid, which is longest? What is its answers above be used to find the measures length? in centimeters?
15. Use your answer from exercise 8 to 16. Use a centimeter ruler to find the perimeter calculate the length of segment LN of triangle IJK to the nearest tenth of a in centimeters. Check by measuring centimeter.with a centimeter ruler.
E
2
5 F
A
B
F
I
J
K N M
C
D
E
S
R
Q
L
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-31-3
ExampleExample
Study Guide and InterventionAngle Measure
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
© Glencoe/McGraw-Hill 19 Glencoe Geometry
Less
on
1-4
Measure Angles If two noncollinear rays have a common endpoint, they form an angle. The rays are the sides of the angle.The common endpoint is the vertex. The angle at the right can be named as �A, �BAC, �CAB, or �1.
A right angle is an angle whose measure is 90. An acute anglehas measure less than 90. An obtuse angle has measure greater than 90 but less than 180.
A C
B
1
a. Name all angles that have R as avertex.Three angles are �1, �2, and �3. Forother angles, use three letters to namethem: �SRQ, �PRT, and �SRT.
b. Name the sides of �1.
RS���, RP���
S R T
PQ
1 2 3
Measure each angle andclassify it as right, acute, or obtuse.
a. �ABDUsing a protractor, m�ABD � 50.50 � 90, so �ABD is an acute angle.
b. �DBCUsing a protractor, m�DBC � 115.180 � 115 � 90, so �DBC is an obtuseangle.
c. �EBCUsing a protractor, m�EBC � 90.�EBC is a right angle.
BA
D E
C
Example 1Example 1 Example 2Example 2
ExercisesExercises
Refer to the figure.
1. Name the vertex of �4.
2. Name the sides of �BDC.
3. Write another name for �DBC.
Measure each angle in the figure and classify it as right,acute, or obtuse.
4. �MPR
5. �RPN
6. �NPS
P
NM
R
S
C
BA
12
34
D
© Glencoe/McGraw-Hill 20 Glencoe Geometry
Congruent Angles Angles that have the same measure are congruent angles. A ray that divides an angle into two congruent angles is called an angle bisector. In the figure, PN��� is the angle bisector of �MPR. Point N lies in the interior of �MPR and �MPN � �NPR.
Refer to the figure above. If m�MPN � 2x � 14 and m�NPR � x � 34, find x and find m�MPR.Since PN��� bisects �MPR, �MPN � �NPR, or m�MPN � m�NPR.
2x � 14 � x � 34 m�NPR � (2x � 14) � (x � 34)2x � 14 � x � x � 34 � x � 54 � 54
x � 14 � 34 � 108x � 14 � 14 � 34 � 14
x � 20
QS��� bisects �PQT, and QP��� and QR��� are opposite rays.
1. If m�PQT � 60 and m�PQS � 4x � 14, find the value of x.
2. If m�PQS � 3x � 13 and m�SQT � 6x � 2, find m�PQT.
BA��� and BC��� are opposite rays, BF��� bisects �CBE, and BD��� bisects �ABE.
3. If m�EBF � 6x � 4 and m�CBF � 7x � 2, find m�EBC.
4. If m�1 � 4x � 10 and m�2 � 5x, find m�2.
5. If m�2 � 6y � 2 and m�1 � 8y � 14, find m�ABE.
6. Is �DBF a right angle? Explain.
BA C
F
ED
12 3
4
QP R
TS
P R
NM
Study Guide and Intervention (continued)
Angle Measure
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
ExampleExample
ExercisesExercises
Skills PracticeAngle Measure
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
© Glencoe/McGraw-Hill 21 Glencoe Geometry
Less
on
1-4
For Exercises 1–12, use the figure at the right.
Name the vertex of each angle.
1. �4 2. �1
3. �2 4. �5
Name the sides of each angle.
5. �4 6. �5
7. �STV 8. �1
Write another name for each angle.
9. �3 10. �4
11. �WTS 12. �2
Measure each angle and classify it as right, acute,or obtuse.
13. �NMP 14. �OMN
15. �QMN 16. �QMO
ALGEBRA In the figure, BA��� and BC��� are opposite rays,BD��� bisects �EBC, and BF��� bisects �ABE.
17. If m�EBD � 4x � 16 and m�DBC � 6x � 4,find m�EBD.
18. If m�ABF � 7x � 8 and m�EBF � 5x � 10,find m�EBF.
B CA
FE
D
M NL
Q O
P
U
T
VW
S5 3
21
4
© Glencoe/McGraw-Hill 22 Glencoe Geometry
For Exercises 1–10, use the figure at the right.
Name the vertex of each angle.
1. �5 2. �3
3. �8 4. �NMP
Name the sides of each angle.
5. �6 6. �2
7. �MOP 8. �OMN
Write another name for each angle.
9. �QPR 10. �1
Measure each angle and classify it as right, acute,or obtuse.
11. �UZW 12. �YZW
13. �TZW 14. �UZT
ALGEBRA In the figure, CB��� and CD��� are opposite rays,CE��� bisects �DCF, and CG��� bisects �FCB.
15. If m�DCE � 4x � 15 and m�ECF � 6x � 5,find m�DCE.
16. If m�FCG � 9x � 3 and m�GCB � 13x � 9,find m�GCB.
17. TRAFFIC SIGNS The diagram shows a sign used to warn drivers of a school zone or crossing. Measure and classify each numbered angle. 2
1
B
C
G
F
ED
Z YT
U
V W
X
N
O
PQ
R
M12
8
3
54
6
7
Practice Angle Measure
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
Reading to Learn MathematicsAngle Measure
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
© Glencoe/McGraw-Hill 23 Glencoe Geometry
Less
on
1-4
Pre-Activity How big is a degree?
Read the introduction to Lesson 1-4 at the top of page 29 in your textbook.• A semicircle is half a circle. How many degrees are there in a
semicircle?• How many degrees are there in a quarter circle?
Reading the Lesson1. Match each description in the first column with one of the terms in the second column.
Some terms in the second column may be used more than once or not at all.a. a figure made up of two noncollinear rays with a 1. vertex
common endpoint 2. angle bisectorb. angles whose degree measures are less than 90 3. opposite raysc. angles that have the same measure 4. angled. angles whose degree measures are between 90 and 180 5. obtuse anglese. a tool used to measure angles 6. congruent anglesf. the common endpoint of the rays that form an angle 7. right anglesg. a ray that divides an angle into two congruent angles 8. acute angles
9. compass10. protractor
2. Use the figure to name each of the following.a. a right angleb. an obtuse anglec. an acute angled. a point in the interior of �EBCe. a point in the exterior of �EBAf. the angle bisector of �EBCg. a point on �CBEh. the sides of �ABFi. a pair of opposite raysj. the common vertex of all angles shown in the figurek. a pair of congruent anglesl. the angle with the greatest measure
Helping You Remember3. A good way to remember related geometric ideas is to compare them and see how they
are alike and how they are different. Give some similarities and differences betweencongruent segments and congruent angles.
B G
28�28�
A
EF
CD
© Glencoe/McGraw-Hill 24 Glencoe Geometry
Angle RelationshipsAngles are measured in degrees (�). Each degree of an angle is divid-ed into 60 minutes (�), and each minute of an angle is divided into 60 seconds ().
60� � 1�
60 � 1�
67�12�� � 67�30�
70.4� � 70°24�
90� � 89°60�
Two angles are complementary if the sum of their measures is 90�.Find the complement of each of the following angles.
1. 35�15� 2. 27�16� 3. 15�54�
4. 29�18�22 5. 34�29�45 6. 87�2�3
Two angles are supplementary if the sum of their measures is 180�.Find the supplement of each of the following angles.
7. 120�18� 8. 84�12� 9. 110�2�
10. 45�16�24 11. 39�21�54 12. 129�18�36
13. 98�52�59 14. 9�2�32 15. 1�2�3
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-41-4
Study Guide and InterventionAngle Relationships
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
© Glencoe/McGraw-Hill 25 Glencoe Geometry
Less
on
1-5
Pairs of Angles Adjacent angles are angles in the same plane that have a commonvertex and a common side, but no common interior points. Vertical angles are twononadjacent angles formed by two intersecting lines. A pair of adjacent angles whosenoncommon sides are opposite rays is called a linear pair.
Identify each pair of angles as adjacent angles, vertical angles,and/or as a linear pair.
ExampleExample
a.
�SRT and �TRU have a commonvertex and a common side, but nocommon interior points. They areadjacent angles.
c.
�6 and �5 are adjacent angles whosenoncommon sides are opposite rays.The angles form a linear pair.
D
CBA
5 6
RU
TS
b.
�1 and �3 are nonadjacent angles formedby two intersecting lines. They are verticalangles. �2 and �4 are also vertical angles.
d.
�A and �B are two angles whose measureshave a sum of 90. They are complementary.�F and �G are two angles whose measureshave a sum of 180. They are supplementary.
AB
FG
30�
60�
60�120�
N
RP
SM
14
32
ExercisesExercises
Identify each pair of angles as adjacent, vertical, and/or as a linear pair.
1. �1 and �2 2. �1 and �6
3. �1 and �5 4. �3 and �2
For Exercises 5–7, refer to the figure at the right.
5. Identify two obtuse vertical angles.
6. Identify two acute adjacent angles.
7. Identify an angle supplementary to �TNU.
8. Find the measures of two complementary angles if the difference in their measures is 18.
R S
NU
T
V
R
S
TU
V
P
Q5
432
1 6
© Glencoe/McGraw-Hill 26 Glencoe Geometry
Perpendicular Lines Lines, rays, and segments that form four right angles are perpendicular. The right angle symbol indicates that the lines are perpendicular. In the figure at the right, AC��� is perpendicular to BD���,or AC��� ⊥ BD���.
Find x so that D�Z� ⊥ P�Z�.If D�Z� ⊥ P�Z�, then m�DZP � 90.
m�DZQ � m�QZP � m�DZP Sum of parts � whole
(9x � 5) � (3x � 1) � 90 Substitution
12x � 6 � 90 Simplify.12x � 84 Subtract 6 from each side.
x � 7 Divide each side by 12.
1. Find x and y so that NR��� ⊥ MQ���.
2. Find m�MSN.
3. m�EBF � 3x � 10, m�DBE � x, and BD��� ⊥ BF���. Find x.
4. If m�EBF � 7y � 3 and m�FBC � 3y � 3, find y so that EB��� ⊥ BC���.
5. Find x, m�PQS, and m�SQR.
6. Find y, m�RPT, and m�TPW.
P
S
V
R
W
T(4y � 5)�
(2y � 5)�
Q R
P S3x �
(8x � 2)�
B CA
DE
F
M
N
R
S Q
P
x �5x �
(9y � 18)�
Z
D
P
Q(9x � 5)�
(3x � 1)�
B
CD
A
Study Guide and Intervention (continued)
Angle Relationships
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
ExampleExample
ExercisesExercises
Skills PracticeAngle Relationships
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
© Glencoe/McGraw-Hill 27 Glencoe Geometry
Less
on
1-5
For Exercises 1–6, use the figure at the right and a protractor.
1. Name two acute vertical angles.
2. Name two obtuse vertical angles.
3. Name a linear pair.
4. Name two acute adjacent angles.
5. Name an angle complementary to �EKH.
6. Name an angle supplementary to �FKG.
7. Find the measures of an angle and its complement if one angle measures 18 degreesmore than the other.
8. The measure of the supplement of an angle is 36 less than the measure of the angle.Find the measures of the angles.
ALGEBRA For Exercises 9–10, use the figure at the right.
9. If m�RTS � 8x � 18, find x so that TR��� ⊥ TS���.
10. If m�PTQ � 3y � 10 and m�QTR � y, find y so that �PTR is a right angle.
Determine whether each statement can be assumed from the figure. Explain.
11. �WZU is a right angle.
12. �YZU and �UZV are supplementary.
13. �VZU is adjacent to �YZX.
ZX
W
V
Y
U
TP
QR
S
K
G
J
FE
H
© Glencoe/McGraw-Hill 28 Glencoe Geometry
For Exercises 1–4, use the figure at the right and a protractor.
1. Name two obtuse vertical angles.
2. Name a linear pair whose vertex is B.
3. Name an angle not adjacent to but complementary to �FGC.
4. Name an angle adjacent and supplementary to �DCB.
5. Two angles are complementary. The measure of one angle is 21 more than twice themeasure of the other angle. Find the measures of the angles.
6. If a supplement of an angle has a measure 78 less than the measure of the angle, whatare the measures of the angles?
ALGEBRA For Exercises 7–8, use the figure at the right.
7. If m�FGE � 5x � 10, find x so that FC��� ⊥ AE���.
8. If m�BGC � 16x � 4 and m�CGD � 2x � 13,find x so that �BGD is a right angle.
Determine whether each statement can be assumed from the figure. Explain.
9. �NQO and �OQP are complementary.
10. �SRQ and �QRP is a linear pair.
11. �MQN and �MQR are vertical angles.
12. STREET MAPS Darren sketched a map of the cross streets nearest to his home for his friend Miguel. Describe two different anglerelationships between the streets. Olive
Beac
on
Main
Q
O
P
RS
M
N
GF
AB
E
D
C
DA
E
HG
B C
F
Practice Angle Relationships
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
Reading to Learn MathematicsAngle Relationships
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
© Glencoe/McGraw-Hill 29 Glencoe Geometry
Less
on
1-5
Pre-Activity What kinds of angles are formed when streets intersect?
Read the introduction to Lesson 1-5 at the top of page 37 in your textbook.
• How many separate angles are formed if three lines intersect at a commonpoint? (Do not use an angle whose interior includes part of another angle.)
• How many separate angles are formed if n lines intersect at a commonpoint? (Do not count an angle whose interior includes part of another angle.)
Reading the Lesson1. Name each of the following in the figure at the right.
a. two pairs of congruent angles
b. a pair of acute vertical angles
c. a pair of obtuse vertical angles
d. four pairs of adjacent angles
e. two pairs of vertical angles
f. four linear pairs
g. four pairs of supplementary angles
2. Tell whether each statement is always, sometimes, or never true.
a. If two angles are adjacent angles, they form a linear pair.
b. If two angles form a linear pair, they are complementary.
c. If two angles are supplementary, they are congruent.
d. If two angles are complementary, they are adjacent.
e. When two perpendicular lines intersect, four congruent angles are formed.
f. Vertical angles are supplementary.
g. Vertical angles are complementary.
h. The two angles in a linear pair are both acute.
i. If two angles form a linear pair, one is acute and the other is obtuse.
3. Complete each sentence.
a. If two angles are supplementary and x is the measure of one of the angles, then themeasure of the other angle is .
b. If two angles are complementary and x is the measure of one of the angles, then themeasure of the other angle is .
Helping You Remember4. Look up the nonmathematical meaning of supplementary in your dictionary. How can
this definition help you to remember the meaning of supplementary angles?
65� 2 34
1
© Glencoe/McGraw-Hill 30 Glencoe Geometry
Curve StitchingThe star design at the right was created by a method known as curve stitching. Although the design appears to contain curves, it is made up entirely of line segments.
To begin the star design, draw a 60° angle. Mark eight equally-spaced points on each ray, and number the points as shown below. Then connect pairs of points that have the same number.
To make a complete star, make the same design in six 60° angles that have a common central vertex.
1. Complete the section of the star design above by connecting pairs of points that have the same number.
2. Complete the following design.
3. Create your own design. You may use several angles, and the angles may overlap.
1 2 3 4 5 6 7 8 9
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Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-51-5
Study Guide and InterventionPolygons
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
© Glencoe/McGraw-Hill 31 Glencoe Geometry
Less
on
1-6
Polygons A polygon is a closed figure formed by a finite number of coplanar linesegments. The sides that have a common endpoint must be noncollinear and each sideintersects exactly two other sides at their endpoints. A polygon is named according to itsnumber of sides. A regular polygon has congruent sides and congruent angles. A polygoncan be concave or convex.
Name each polygon by its number of sides. Then classify it asconcave or convex and regular or irregular.
ExampleExample
a.
The polygon has 4 sides, so it is a quadrilateral.It is concave because part of D�E� or E�F� lies in theinterior of the figure. Because it is concave, itcannot have all its angles congruent and so it isirregular.
c.
The polygon has 5 sides, so it is a pentagon. It isconvex. All sides are congruent and all angles arecongruent, so it is a regular pentagon.
D F
G
E b.
The figure is not closed, so it isnot a polygon.
d.
The figure has 8 congruent sidesand 8 congruent angles. It isconvex and is a regular octagon.
H
J K
LI
ExercisesExercises
Name each polygon by its number of sides. Then classify it as concave or convexand regular or irregular.
1. 2. 3.
4. 5. 6.
© Glencoe/McGraw-Hill 32 Glencoe Geometry
Perimeter The perimeter of a polygon is the sum of the lengths of all the sides of thepolygon. There are special formulas for the perimeter of a square or a rectangle.
Write an expression or formula for the perimeter of each polygon.Find the perimeter.
Study Guide and Intervention (continued)
Polygons
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
ExampleExample
a.
P � a � b � c� 3 � 4 � 5� 12 in.
b.
P � 4s� 4(5)� 20 cm
c.
P � 2� � 2w� 2(3) � 2(2)� 10 ft
3 ft
2 ft
�
�
w w
5 cm
5 cm 5 cm
5 cm
s
s
s s3 in.5 in.
4 in.
a
b
c
ExercisesExercises
Find the perimeter of each figure.
1. 2.
3. 4.
Find the length of each side of the polygon for the given perimeter.
5. P � 96 6. P � 48x
x
2x
x � 2
rectangle
2x
x
1 cm
24 yd
19 yd
12 yd 14 yd
27 yd
square
5.5 ft
3.5 cm
3 cm2.5 cm
Skills PracticePolygons
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
© Glencoe/McGraw-Hill 33 Glencoe Geometry
Less
on
1-6
Name each polygon by its number of sides and then classify it as convex orconcave and regular or irregular.
1. 2. 3.
4. 5. 6.
Find the perimeter of each figure.
7. 8. 9.
COORDINATE GEOMETRY Find the perimeter of each polygon.
10. triangle ABC with vertices A(3, 5), B(3, 1), and C(0, 1)
11. quadrilateral QRST with vertices Q(�3, 2), R(1, 2), S(1, �4), and T(�3, �4)
12. quadrilateral LMNO with vertices L(�1, 4), M(3, 4), N(2, 1), and O(�2, 1)
ALGEBRA Find the length of each side of the polygon for the given perimeter.
13. P � 104 millimeters 14. P � 84 kilometers 15. P � 88 feet4w � 1
w
10 in.
10 in.2 in. 2 in.
2 in.2 in.2 in. 2 in.
5 m2 m 3 m
6 m4 m
40 yd
20 yd
18 yd 20 yd
© Glencoe/McGraw-Hill 34 Glencoe Geometry
Name each polygon by its number of sides and then classify it as convex orconcave and regular or irregular.
1. 2. 3.
Find the perimeter of each figure.
4. 5. 6.
COORDINATE GEOMETRY Find the perimeter of each polygon.
7. quadrilateral OPQR with vertices O(�3, 2), P(1, 5), Q(6, 4), and R(5, �2)
8. pentagon STUVW with vertices S(0, 0), T(3, �2), U(2, �5), V(�2, �5), and W(�3, �2)
ALGEBRA Find the length of each side of the polygon for the given perimeter.
9. P � 26 inches 10. P � 39 centimeters 11. P � 89 feet
SEWING For Exercises 12–13, use the following information.Jasmine plans to sew fringe around the scarf shown in the diagram.
12. How many inches of fringe does she need to purchase?
13. If Jasmine doubles the width of the scarf, how many inches of fringe will she need?
16 in.
4 in. 4 in.
16 in.
2x � 2
x � 9
5x � 4
3x � 5
2x � 3
6n � 8
n
14 cm
14 cm
4 cm
4 cm 6 cm6 cm
6 cm2 cm
32 mi
33 mi21 mi
7 mm
10 mm18 mm
18 mm
Practice Polygons
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
Reading to Learn MathematicsPolygons
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
© Glencoe/McGraw-Hill 35 Glencoe Geometry
Less
on
1-6
Pre-Activity How are polygons related to toys?
Read the introduction to Lesson 1-6 at the top of page 45 in your textbook.
Name four different shapes that can each be formed by four sticks connected toform a closed figure. Assume you have sticks with a good variety of lengths.
Reading the Lesson
1. Tell why each figure is not a polygon.
a. b. c.
2. Name each polygon by its number of sides. Then classify it as convex or concave andregular or not regular.
a. b. c.
3. What is another name for a regular quadrilateral?
4. Match each polygon in the first column with the formula in the second column that canbe used to find its perimeter. (s represents the length of each side of a regular polygon.)
a. regular dodecagon i. P � 8s
b. square ii. P � 6s
c. regular hexagon iii. P � a � b � c
d. rectangle iv. P � 12s
e. regular octagon v. P � 2� � 2w
f. triangle vi. P � 4s
Helping You Remember
5. One way to remember the meaning of a term is to explain it to another person.How would you explain to a friend what a regular polygon is?
© Glencoe/McGraw-Hill 36 Glencoe Geometry
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
1-61-6
Perimeter and Area of Irregular ShapesTwo formulas that are used frequently in mathematics are perimeter andarea of a rectangle.
Perimeter: P � 2� � 2wArea: A � �w, where � is the length and w is the width
However, many figures are combinations of two or more rectangles creatingirregular shapes. To find the area of an irregular shape, it helps to separatethe shape into rectangles, calculate the formula for each rectangle, then findthe sum of the areas.
Find the area of thefigure at the right.Separate the figure into two rectangles.
A � �wA1 � 9 2 A2 � 3 3
� 18 � 9
18 � 9 � 27
The area of the irregular shape is 27 m2.
Find the area and perimeter of each irregular shape.
1. 2.
3.4.
For Exercises 5–8, find the perimeter of the figures in Exercises 1–4.
5. 6. 7. 8.
9. Describe the steps you used to find the perimeter in Exercise 1.
9 ft
2 ft
3 ft
7 ft
6 ft
4 ft
8 cm
4 cm
2 cm
2 cm
4 cm
4 cm
6 cm
4 cm
9 m
26 m
6 m13 m
7 m
12 m
2 in.
4 in. 4 in.
1 in.
9 m
3 m
1
25 m
2 m
9 m
3 m
5 m
2 m
ExampleExample
Chapter 1 Test, Form 111
© Glencoe/McGraw-Hill 37 Glencoe Geometry
Ass
essm
ents
Write the letter for the correct answer in the blank at the right of each question.
1. Name the geometric shape modeled by a pinhole in a wall.A. line segment B. plane C. line D. point
For Questions 2–4, use the figure given at the right.
2. Which is another name for line �?A. AB��� B. BD���
C. C D. P
3. Name the intersection of lines � and m.A. A B. BC. C D. P
4. Name three points coplanar with point A.A. B, C, F B. E, F, GC. B, C, E D. B, D, G
5. Find the length of R�S�.A. 33 mm B. 34 mmC. 35 mm D. 36 mm
6. Find the precision for a measurement of 72 centimeters.A. 0.5 cm B. 0.1 cmC. 1 mm D. 0.5 mm
7. Find the length of B�C�.A. 12 cm B. 13 cmC. 25 cm D. 38 cm
8. Use the number line to find MN.A. �5 B. 1C. 5 D. 10
For Questions 9 and 10, use the figure given at the right.
9. Find the distance between points P and Q.A. 5 B. 7C. 9 D. 25
10. Find the coordinates of the midpoint of P�Q�.
A. �2, 3�12�� B. �0, 3�
12�� C. (0, 3) D. �3�
12�, 0�
x
y
O
P
Q
�5 �4 �3 �2 �1 0 1 2 3
M N
A C
25 cm
13 cm B
1cm 2 3 4
R S
�
P
m
AB
C
D
E
G
F
1.
2.
3.
4.
5.
6.
7.
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9.
10.
NAME DATE PERIOD
SCORE
NAME DATE PERIOD
© Glencoe/McGraw-Hill 38 Glencoe Geometry
Chapter 1 Test, Form 1 (continued)11
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
For Questions 11–13, use the figure at the right.
11. Which point is the vertex of all the angles in this figure?A. A B. BC. C D. E
12. What type of angle is �ABC?A. acute angle B. right angle C. obtuse angle D. straight angle
13. Which is true?A. m�EBF � 140 B. m�EBF � 90 C. m�EBF � 50 D. m�EBF � 40
14. For what value of x is �ATK � �MJS if m�ATK � 5x � 4 and m�MJS � 8x � 11?A. 29 B. 15 C. 10 D. 5
For Questions 15–17, use the figure at the right.
15. Which pair of angles are vertical angles?A. �RST, �TSU B. �RSX, �TSUC. �TSU, �USV D. �RSX, �XSW
16. Which angle is supplementary to �USV ?A. �TSU B. �VSW C. �RSV D. �WSR
17. Find x and y.A. x � 10, y � 12 B. x � 20, y � 7 C. x � 10, y � 8 D. x � 50, y � 40
For Questions 18–20, use the figures below.
18. Which figure is not a polygon?A. Figure A B. Figure B C. Figure C D. Figure D
19. Find the perimeter of the convex pentagon.A. 46 cm B. 50 cm C. 61 cm D. 72 cm
20. Suppose the length and width of the rectangle are doubled. What is itsperimeter?A. 120 cm B. 92 cm C. 76 cm D. 46 cm
Bonus Each side of a square is 2x � 6 yards long. If the perimeter of the square is 72 yards what is the value of x?
8 cm
8 cm
8 cm
4 cm
15 cm15 cm
18 cm
18 cm
25 cm
15 cm
8 cm8 cm
15 cm
12 cm
15 cm12 cmFigure A Figure DFigure B Figure C
25 cm
SRX W V
U
T
5x �4x �
(10y � 10)�
B DA
C
EF
50�
B:
Chapter 1 Test, Form 2A11
© Glencoe/McGraw-Hill 39 Glencoe Geometry
Ass
essm
ents
Write the letter for the correct answer in the blank at the right of each question.
1. How many planes can be drawn through any three noncollinear points?A. 0 B. 1 C. 2 D. 3
For Questions 2 and 3, use the figure at the right.
2. Which three points in the figure are collinear?A. A, B, D B. E, C, AC. A, B, C D. F, E, G
3. Name the intersection of the plane P and the plane that contains points B, C, and D.A. point B B. B�D�
C. BC��� D. triangle BCD
4. Find the length of R�S�.
A. 1�156� in. B. 1�
38� in.
C. 1�176� in. D. 1�
58� in.
5. Find the precision for a measurement of 18�12� feet.
A. �12� ft B. �
14� ft C. �
18� ft D. 1 in.
6. Find the length of P�Q�.A. 50.9 cm B. 46.3 cmC. 25.7 cm D. 21.3 cm
7. Find y if B is between A and C, AB is 2y, BC is 6y, and AC is 48.A. 24 B. 8 C. 6 D. 4
8. Find the distance between P(2, 8) and Q(5, 3).A. 9 B. �18� C. �34� D. �170�
9. Find the coordinates of the midpoint of L�B� if L(8, 5) and B(�6, 2).
A. �1, 3�12�� B. �2, 1�
12�� C. �7, 3�
12�� D. �7, 1�
12��
10. Find the coordinates of T given that S is the midpoint of R�T�, R(�4, 2),and S(6, 8).A. (�14, �4) B. (16, 14) C. (2, 10) D. (1, 5)
P R
38.3 cm
12.6 cmQ
1 2in.
R S
PAB
CE
F
D
G
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 40 Glencoe Geometry
Chapter 1 Test, Form 2A (continued)11
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
For Questions 11 and 12, use the figure at the right.
11. What type of angle is �ABC?A. acute angle B. right angleC. obtuse angle D. straight angle
12. Use a protractor to measure the angles in the figure.Which segment is an angle bisector?A. G�E� B. B�C� C. E�D� D. E�F�
For Questions 13–17, use the figure at the right.
13. Find m�FBD if �FBD and �DBE are complementary and m�FBD is twice m�DBE.A. 30 B. 45C. 60 D. 90
14. Which pair of angles are supplementary?A. �ABE, �CBD B. �ABC, �ABD C. �ABC, �CBD D. �ABC, �EBD
15. Which angle is a vertical angle to �ABE?A. �DBE B. �CBD C. �ABC D. �EBA
16. If m�CBF � 6x � 18, find x so that CB ⊥ BF.A. 90 B. 45 C. 18 D. 12
17. Find m�ABC if m�ABC � 4x � 9 and m�EBD � 7x � 9.A. 6 B. 33 C. 45 D. 73
For Questions 18 and 19, use the figure at the right.
18. Which describes this figure?A. hexagon, concave, not regularB. pentagon, concave, regularC. hexagon, convex, not regularD. not a polygon
19. What is x for a perimeter of 108 kilometers?A. 53 B. 15 C. 18 D. 105
20. A rectangle has a length of 1.4 feet and a width of 1.2 feet. What is the effecton the perimeter of this rectangle if the length and width are doubled?A. The perimeter is doubled. B. The perimeter is increased by 8.C. The perimeter is multiplied by 4. D. The perimeter is tripled.
Bonus Find m�A if �A is complementary to �B, �B is supplementary to �C, m�B � 15x � 2, and m�C � 25x � 22.
(x � 3) km
F
DE
B
AC
A B
C
DE
F
G
B:
NAME DATE PERIOD
Chapter 1 Test, Form 2B11
© Glencoe/McGraw-Hill 41 Glencoe Geometry
Ass
essm
ents
Write the letter for the correct answer in the blank at the right of each question.
1. Suppose A and B are points. How many lines contain both A and B?A. 0 B. 1C. 2 D. 3
For Questions 2 and 3, use the figure at the right.
2. Which three points in the figure are collinear?A. C, D, F B. B, C, DC. A, E, F D. A, D, E
3. Name the intersection of the plane that containspoints A, B, and D and the plane P.A. point D B. A�D�
C. triangle BCD D. BD���
4. Find the length of X�Y�.
A. 1�1116� in. B. 1�
58� in.
C. 1�196� in. D. 1�
12� in.
5. Find the precision for a measurement of 34.0 centimeters.A. 0.5 cm B. 1 mm C. 0.5 mm D. 1 cm
6. Find the length of H�J�.A. 11.3 cm B. 12.3 cmC. 13.7 cm D. 45.9 cm
7. Find x if S is between R and T, RS is x � 3, ST is 5x, and RT is 57.A. 9 B. 10 C. 10.8 D. 12
8. Find the distance between M(�2, 3) and N(8, 2).
A. 8 B. �61� C. 10 D. �101�
9. Find the coordinates of the midpoint of A�S� if A(�4, 7) and S(5, 3).
A. (1, 10) B. ��4�12�, 2� C. ��
12�, 5� D. ���
12�, 5�
10. Find the coordinates of T given that S is the midpoint of R�T�, R(2, 6),and S(�2, 0).A. (6, 12) B. (�6, �6) C. (0, 3) D. (�2, 3)
G J
29.1 cm
16.8 cm H
1 2in.
X Y
PCB
D
E
F
A
1.
2.
3.
4.
5.
6.
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8.
9.
10.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 42 Glencoe Geometry
Chapter 1 Test, Form 2B (continued)11
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
For Questions 11 and 12, use the figure at the right.
11. What type of angle is �BAC?A. acute angle B. right angleC. obtuse angle D. straight angle
12. Use a protractor to measure the angles in the figure.Which segment is an angle bisector?A. A�B� B. C�D� C. C�B� D. A�E�
For Questions 13–17, use the figure at the right.
13. Find m�VSW if �WSR and �VSW are complementaryand m�WSR is four times m�VSW.A. 72 B. 36C. 22.5 D. 18
14. Which pair of angles are supplementary?A. �USV, �VSW B. �VSW, �WSR C. �TSV, �VSW D. �TSR, �USW
15. Which angle is a vertical angle to �UST?A. �VSW B. �USV C. �TSR D. �WSR
16. If m�VSR � 8x � 18, find x so that U�S� ⊥ V�S�.A. 9 B. 12.25 C. 72 D. 90
17. Find m�USW if m�USW � 7x � 34 and m�TSR � 4x � 29.A. 147 B. 113 C. 84 D. 21
For Questions 18 and 19, use the figure at the right.
18. Which describes this figure?A. hexagon, convex, regularB. pentagon, concave, regularC. pentagon, convex, not regularD. not a polygon
19. What is y for a perimeter of 100 feet?A. 5 B. 15 C. 17 D. 23
20. A square has sides with a length of 5.8 inches. What is the effect on theperimeter of this square if the sides are tripled?A. The perimeter stays the same. B. The perimeter is increased by 12.C. The perimeter is multiplied by 3. D. The perimeter is multiplied by 9.
Bonus Find m�A if �A is supplementary to �B, �B is supplementary to �C, m�B � 12x � 8, and m�C � 8x � 8.
y � 5
y
R
T
U
V W
S
FE
D
CA
B
B:
NAME DATE PERIOD
Chapter 1 Test, Form 2C11
© Glencoe/McGraw-Hill 43 Glencoe Geometry
Ass
essm
ents
For Questions 1–4, use the figure at the right.
1. What is another name for line �?
2. Name three points on plane P.
3. Name the intersection of planes P and N.
4. Name three noncoplanar points.
For Questions 5 and 6,use the figure at theright.
5. What is the length ofA�B�?
6. What is the precision of your measurement of A�B�?
7. Find the length of D�E� if D is between points C and E,CD � 6.5 centimeters, and CE � 13.8 centimeters.
8. Find the length of X�Z�.
9. Find x if R�S� � S�T�.
For Questions 10–12, use the coordinate grid.
10. Find the distance between A and B.
11. Find the coordinates of the midpoint of C�D�.
12. Find the coordinates of a point E if Cis the midpoint of A�E�.
13. The vertices of a triangle are located at P(0, 0), Q(8, 6), andR(�3, 4). What is the perimeter of this triangle?
14. Find x and y if U�V� bisects T�W� and UV � 40.
ZT W
U
V
3y � 1
2y � 6
3y � 13x � 2
x
y
O
B
D
A
C
R T
52 in.
6x � 8 S
X Z
4x � 3
2x � 78 cm Y
1cm 2 3 4 5 6
A B
�
P
N
CA B
DE
F
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 44 Glencoe Geometry
Chapter 1 Test, Form 2C (continued)11
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
15. Measure �PQR. Then classify �PQRas right, acute, or obtuse.
In the figure, EA��� and EB��� are opposite rays and EC��� bisects �FEG.
16. Find x if m�FEG � 82, and m�FEC � 5x � 11.
17. If m�AED � 16y � 10, find y so that E�D� ⊥ A�B�.
For Questions 18–21, use the figure at the right.
18. Find y.
19. Find m�1.
20. Find m�2.
21. Find x .
For Questions 22–25, use the polygons at the right.
22. Name polygon ABCDEF by its sides. Then classify it asconvex or concave and regular or not regular.
23. Find the perimeter of polygon ABCDEF for x � 4.
24. Find the length of each side of polygon RST.
25. Find the length of one side of a regular pentagon whoseperimeter is the same as the perimeter of RST.
Bonus Find the dimensions of a rectangle whose length is 3 more than twice its width and has a perimeter of 30 centimeters.
6x � 53y � 1
2y � 11
A D
B C R
F E T S
40�
72�1
2
(11x � 24)�
(8y � 16)�
BA
D
GC
F
E
R
P
Q
NAME DATE PERIOD
Chapter 1 Test, Form 2D11
© Glencoe/McGraw-Hill 45 Glencoe Geometry
Ass
essm
ents
For Questions 1–4, use the figure at the right.
1. What is another name for line m?
2. Name three points on plane B.
3. Name the intersection of planes A and B.
4. Name three noncollinear points.
For Questions 5 and 6, use the figure at the right.
5. What is the length of Q�R�?
6. What is the precision of your measurement of Q�R�?
7. Find the length of L�O� if O is between points L and M,LM � 18.6 centimeters, and OM � 12.9 centimeters.
8. Find the length of D�E�.
9. Find y if X�Y� � Y�Z�.
For Questions 10–12, use the coordinate grid.
10. Find the distance between Land M.
11. Find the coordinates of the midpoint of M�N�.
12. Find the coordinates of a point Q if P is the midpoint of N�Q�.
13. The vertices of a triangle are located at P(0, 6), Q(8, 12), andR(3, �3). What is the perimeter of this triangle?
14. Find x if R�S� bisects A�B� and RS � 36.
TA B
R
S
18
2y � 6
2y � 525 � 3x
x
y
O
M
NPL
X Z
5y � 11
23 in. Y
D F
24 cm
5x � 133x � 5 E
1 2in.
Q R
A
B
m
T
R
SU
YZ
X
V
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 46 Glencoe Geometry
Chapter 1 Test, Form 2D (continued)11
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
15. Measure �ABC. Then classify �ABC as right, acute, or obtuse.
In the figure, RC��� and RD��� are opposite rays and RQ��� bisects �WRV.
16. Find y if m�WRQ � 48 and m�QRV � 7y � 6.
17. Find x so that C�R� ⊥ P�R�.
For Questions 18–21, use the figure at the right.
18. Find x.
19. Find m�1.
20. Find m�2.
21. Find y.
For Questions 22–25, use the polygons at the right.
22. Name polygon RSTUVby its sides. Then classify it as convex orconcave and regular or not regular.
23. Find the perimeter of polygon RSTUV for y � 9.
24. Find the length of each side of polygon ABCD.
25. Find the length of the sides of a regular triangle whoseperimeter is the same as the perimeter of ABCD.
Bonus Find the lengths of the sides of a triangle whose perimeter is 37. The measure of the first side of thetriangle is 8 less than the second side, and the second side is twice the length of the third side.
5y � 8
8x � 3
27 � 4x
S
R T
U D C
A B
V
(9x � 5)� 58�1
2(7y � 27)�
DR
P
C
WQ V
(13x � 12)�
C
A
B
NAME DATE PERIOD
Chapter 1 Test, Form 311
© Glencoe/McGraw-Hill 47 Glencoe Geometry
Ass
essm
ents
For Questions 1–3, use the figure at the right.
1. Name five planes shown in the figure.
2. Name a line that is coplanar with AD��� and AB���.
3. Name the intersection of plane P and the plane that containspoints A, B, and E.
For Questions 4 and 5, usethe figure at the right.
4. Find the length of A�B�.
5. Find the precision for the measurement of A�B�.
6. Find two possible lengths for C�D� if C, D, and E are collinear,CE � 15.8 centimeters, and DE � 3.5 centimeters.
7. Find the length of R�S� if S is between R and T, the length of R�S� is �
13� the length of R�T�, RS � 3x � 3, and ST � 2x � 6.
8. Find y if AC � 3y � 5, CB � 4y � 1, AB � 9y � 12, and pointC lies between A and B.
For Questions 9–11, use the coordinate grid at the right.
9. Find the distance between A and B.
10. Find two possible coordinates of a point D on a line containing A�B� so that AD � �
14�AB.
11. Find two values of y for C located at (1, y) and AC � 5.
x
y
O
B
A
6 7in.
A B
P
A
E
F
D
C
B
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 48 Glencoe Geometry
Chapter 1 Test, Form 3 (continued)11
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
12. Find y if S is the midpoint of R�T�, T is the midpoint of R�U�,RS � 6x � 5, ST � 8x � 1, and TU � 11y � 13.
13. Find all values of x that will make �A an obtuse angle givenm�A � 12x � 6.
14. Find m�RST if ST��� bisects �RSU and SU��� bisects �TSV.
15. Find m�1 if �1 is complementary to �2, �2 is supplementaryto �3, and m�3 � 126.
16. Find y if XW��� ⊥ XZ���, Y is in the interior of �WXZ,m�WXY � 6y � 3, and m�YXZ � 4y � 13.
17. Find the length of L�M� if ON��� is the bisector of L�M� and LN � 3x � 2.
For Questions 18 and 19, use the coordinate grid.
18. Graph polygon ABCD with vertices A(4, 3), B(0, 3), C(�2, 2),and D(�5, 6). Then name polygon ABCD by its number ofsides and classify it as convex or concave and regular orirregular.
19. Find the perimeter of polygon ABCD.
20. Find the perimeter of regular triangle DEF if DE � 28 � 3yand EF � 2y � 3.
Bonus Suppose a regular quadrilateral and a regular triangle havethe same perimeter. The sides of the triangle are 3 incheslonger than the sides of the quadrilateral. Find the lengthsof the sides of the quadrilateral and the triangle.
N ML
O
7x � 1
V
U
T
R
S
(x � 2y � 1)�
(6x � 9)�
(2y � 5)�
NAME DATE PERIOD
Chapter 1 Open-Ended Assessment11
© Glencoe/McGraw-Hill 49 Glencoe Geometry
Ass
essm
ents
Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solution in more than one way orinvestigate beyond the requirements of the problem.
1. Draw and label a figure that shows that plane R contains both lines s andAC��� that intersect at point B. Name three collinear points in plane R.
2. Draw a line on a coordinate plane so that you can determine at least twopoints on the graph. Label those two points D and G.
a. Find the distance between points D and G.
b. Find the coordinates of E, the midpoint of D�G�.
c. Find the coordinates of point H given that G is the midpoint of D�H�.
3. Rectangle WXYZ has a length that is 5 more than three times its width.
a. Draw and label a figure for rectangle WXYZ.
b. Write an algebraic expression for the perimeter of the rectangle.
c. Find the width if the perimeter is 58 millimeters. Explain how you cancheck that your answer is correct.
d. Use a ruler to draw and label P�Q�, which is congruent to the segmentrepresenting the length of rectangle WXYZ. What is the measure of P�Q�?
e. Explain how to find the precision of the measurement of P�Q�.
4. Draw an acute angle, �ABC. Let m�ABC � 6x � 1.
a. Use a protractor to determine the measure of �ABC. Use thismeasure to determine the value of x.
b. Explain how you would determine the measure of an angle that iscomplementary to �ABC.
c. Explain how you would determine the measure of an angle that issupplementary to �ABC.
5. RS��� is in the interior of �TRU, m�TRS � 4x � 6, and m�SRU � 8x � 6.
a. Draw �TRU and RS���.
b. Determine the value of x that will make RS��� an angle bisector. Explainyour steps.
c. Describe the relationship between RU��� and RT��� when x � 7.5.
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 50 Glencoe Geometry
Chapter 1 Vocabulary Test/Review11
Choose from the terms above to complete each sentence.
1. Two lines are if they intersect to form a right angle.
2. Two angles are if their measures have a sum of 90°.
3. When two rays intersect with a common endpoint a(n) is formed.
4. The is the point located halfway between theendpoints of a segment.
5. are nonadjacent angles formed by the intersection oftwo lines.
6. A(n) divides an angle into two congruent angles.
7. Two angles are if their measures have a sum of 180°.
8. Two angles that lie in the same plane are called ifthey share a common side and a common vertex.
9. A(n) is an angle whose measure is less than 90°.
10. Two segments are if they have the same measure.
In your own words—
11. Explain how to find the precision of a measurement of 5�
12� inches on a ruler marked in half inches.
12. Describe what is meant by betweenness of points usingcollinear points M, P, and Q.
?
?
?
?
?
?
?
?
?
? 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
acute angleadjacent anglesangleangle bisectorbetweenness collinearcomplementary concavecongruentconstruction
convexcoplanardegreedistanceexteriorinteriorlineline segmentlinear pairmidpoint
n-gonobtuse angleopposite raysperimeterperpendicularplanepointpolygonprecisionray
regular polygonrelative errorright anglesegment bisectorsidesspacesupplementaryundefined termsvertexvertical angles
NAME DATE PERIOD
SCORE
Chapter 1 Quiz (Lessons 1–1 and 1–2)
11
© Glencoe/McGraw-Hill 51 Glencoe Geometry
Ass
essm
ents
NAME DATE PERIOD
SCORE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
For Questions 1–3, use the figure at the right.
1. What is another name for line �?
2. Name the intersection of lines � and m.
3. Name three collinear points.
For Questions 4 and 5, use the figure at the right.
4. Find the length of A�B�.
5. Find the precision of the measurement of A�B�.
6. Find the length of U�W� if W is between U and V,UV � 16.8 centimeters, and VW � 7.9 centimeters.
7. Find x if RS � 24 centimeters.
8. Find the length of L�O� if M is between L and O, LM � 7x � 9,MO � 14 inches, and LO � 10x � 7.
9. Find x if P�Q� � R�S�, PQ � 9x � 7, and RS � 29.
10. STANDARDIZED TEST PRACTICE Which of the following isnot an undefined term in geometry?A. plane B. point C. bisector D. line
R S
10 cm6x � 4
T
1in.
A B
R T
SU
m
�V
Chapter 1 Quiz (Lesson 1–3)
11
1.
2.
3.
4.
5.
1. Find the coordinates of the midpoint of A�B� for A(2, 5) and B(6, 9).
2. Find the coordinates of D if E is the midpoint of C�D�, for C(�3, 4) and E(0, 1).
3. What is the length of F�H� if G is the midpoint, FG � 12x � 5,and GH � 7x?
4. What is the length of U�V� if WX��� is the segment bisector of U�V� at point Z?
5. STANDARDIZED TEST PRACTICE Find the distance betweenA(�2, 1) and B(4, �3).A. 52 B. �52� C. �20� D. �8�
U
V9x � 2
6x � 8
ZX
W
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 52 Glencoe Geometry
Chapter 1 Quiz (Lessons 1–4 and 1–5)
11
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
For Questions 1–6, use the figure at the right.
1. Name the vertex of �1.
2. Classify �TSV as right, acute, or obtuse.
3. Name a point in the exterior of �RTS.
4. Find m�TSU if S�U� bisects �TSV,m�TSU � 4y � 11, and m�USV � 6y � 5.
5. Name a pair of adjacent angles.
6. Name a pair of vertical angles.
7. Find m�DBC if m�ABC � 5x � 3 and �ABD � �DBC.
For Questions 8 and 9, lines p and q intersect to formadjacent angles 1 and 2.
8. If m�1 � 7x � 6 and m�2 � 8x � 6, find x so that p isperpendicular to q.
9. If m�1 � 4x � 3 and m�2 � 3x � 8, find x so that �1 issupplementary to �2.
10. STANDARDIZED TEST PRACTICE The difference betweentwo complementary angles is 14. Which is the measure of oneof those angles?A. 14 B. 52 C. 83 D. 90
(3x � 2)�B
A
DC
ST
U V
W
PR
1
NAME DATE PERIOD
SCORE
Chapter 1 Quiz (Lesson 1–6)
11
1.
2.
3.
4.
5.
1. Draw a concave pentagon.
2. Find the length of each side of a regular hexagon whoseperimeter is 84 meters.
3. If x � 5, find the perimeter of the rectangle whose length is 6x � 4 and whose width is 3x � 2.
4. The perimeter of a convex pentagon is 15 feet. What is theeffect on its perimeter if each side is doubled?
5. For what value of y is triangle ABC a regular triangle?
7y � 12
5y � 209y � 4
B
CA
NAME DATE PERIOD
SCORE
Chapter 1 Mid-Chapter Test (Lessons 1–1 through 1–3)
11
© Glencoe/McGraw-Hill 53 Glencoe Geometry
Ass
essm
ents
For Questions 1 and 2, use the figure at the right.
1. Which point is coplanar with points A and C?A. A B. BC. C D. D
2. Name the point of intersection of plane M and DE���.A. D B. E C. B D. M
For Questions 3 and 4, use the figure at the right.
3. What is the length of A�B�?
A. about 1�14� in. B. about 1�
12� in.
C. about 1�34� in. D. about 2 in.
4. What is the precision for the measurement of A�B�?
A. 1 in. B. �12� in. C. �
14� in. D. �
18� in.
5. What is the length of T�S�?A. 9.4 cm B. 8.9 cmC. 4.7 cm D. 4.2 cm
R S
8.9 cm
4.7 cm T
1 2in.
A B
MBCA
D
E
6.
7.
8.
9.
10.
NAME DATE PERIOD
SCORE
1.
2.
3.
4.
5.
Part II
For Questions 6–8, use the coordinate grid.
6. Find the distance between R and S.
7. Find the coordinates of the midpoint of T�U�.
8. Find the coordinates of a point M given that U is the midpoint of M�S�.
9. Find y if M is the midpoint of L�N�.
10. In the figure, WZ��� bisects X�Y�. Find the length of X�Y�.
X
Y6x � 11
4x � 5V
Z
W
L N
6y � 59y � 4
M
x
y
O
R US
T
Part I Write the letter for the correct answer in the blank at the right of each question.
© Glencoe/McGraw-Hill 54 Glencoe Geometry
Chapter 1 Cumulative Review(Chapter 1)
11
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
For Questions 1 and 2, use the figure at the right.
1. Name three points that are collinear.(Lesson 1-1)
2. Name the intersection of AE��� and CG���.(Lesson 1-1)
Find the measurement of each segment. Assume that theart is not drawn to scale. (Lesson 1-2)
3. A�B�
4. K�N�
5. Use the Pythagorean Theorem to find the distance betweenA(�12, 13) and B(�2, �11). (Lesson 1-3)
6. Find the coordinates of B if A has coordinates (3, 5) and Y(�2, 3) is the midpoint of A�B�. (Lesson 1-3)
For Questions 7 and 8, use the figure to name the vertex and sides of each angle. Then measure and classify each angle. (Lesson 1-4)
7. �JNK 8. �HNK
For Questions 9–11, use the figure at the right. (Lesson 1-5)
9. Name a pair of supplementarynonadjacent angles.
10. Name two obtuse vertical angles.
11. Name an angle complementary to �CFD.
12. If m�HJK � 7y � 2 and m�PQR � 133, find y so that �HJKis supplementary to �PQR. (Lesson 1-5)
13. Name this polygon by its number of sides and then classify it as convex or concave and regularor irregular. (Lesson 1-6)
14. Find the perimeter of �ABC if A(1, 1), B(4, �3), and C(�3, �2).(Lesson 1-6)
15. Find the length of each side of a regular pentagon whoseperimeter is 90 centimeters. (Lesson 1-6)
A F DE
B C
G60� 30�
120�
N
K
M
J
H
L
157�
77�26�
J K L M N
4 mm 3 mm
A C5 cm
2 cmB
A
C
E
B
D
FG
H
NAME DATE PERIOD
SCORE
Standardized Test Practice (Chapter 1)
© Glencoe/McGraw-Hill 55 Glencoe Geometry
1. Which object models a line? (Lesson 1-1)
A. a fly B. a wall C. a meter stick D. a diskette
2. Which figure shows AB��� and point G contained in plane R ? (Lesson 1-1)
E. F.
G. H.
3. What is the precision of a measurement of 49.5 centimeters on aruler with millimeter marks? (Lesson 1-2)
A. 49 cm to 50 cm B. 49.0 cm to 50.0 cmC. 490 mm to 500 mm D. 494.5 mm to 495.5 mm
4. When segments have the same measure, they are said to be. (Lesson 1-2)
E. accurate F. congruentG. precise H. constructed
5. Find the distance between A(�3, 5) and B(4, 2), to the nearesthundredth. (Lesson 1-3)
A. 6.75 B. 7.62 C. 8.06 D. 10
6. Find EF if E is the midpoint of D�F�, DE � 15 � 3x, and EF � x � 3. (Lesson 1-3)
E. 1 F. 3 G. 6 H. 9
For Questions 7–9, use the figure.
7. What is another name for �2? (Lesson 1-4)
A. �WYX B. �WXYC. �3 D. �Y
8. Which angles form a linear pair? (Lesson 1-5)
E. �1 and �3 F. �2 and �5 G. �2 and �3 H. �1 and �4
9. Name the angle that is vertical to �3. (Lesson 1-5)
A. �1 B. �2 C. �3 D. �4
10. Find the length of one side of a regular hexagon whose perimeteris 75 feet. (Lesson 1-6)
E. 25 ft F. 18.75 ft G. 15 ft H. 12.5 ft
WY
X14
235
?
A
B
G RA B
G
R
A BR
GA BG R
NAME DATE PERIOD
SCORE
Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
Ass
essm
ents
11
© Glencoe/McGraw-Hill 56 Glencoe Geometry
Standardized Test Practice (continued)
11. How many points name a line? (Lesson 1-1)
12. What is the measure of A�C�? (Lesson 1-2)
For Questions 13–15, HL��� bisects �KHI andHG��� and HI��� are opposite rays.
13. If �1 � �2, m�KHG � 70, and m�1 � 3d � 2,find d. (Lesson 1-4)
14. If m�2 � a � 15 and m�3 � a � 35, find a sothat HL��� ⊥ HJ���. (Lesson 1-5)
15. Find m�4, if m�GHL � 125. (Lesson 1-5)
G H I
J
KL
1 42 3
A B C3.7 5.2
NAME DATE PERIOD
Part 2: Grid In
Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.
Part 3: Short Response
Instructions: Show your work or explain in words how you found your answer.
11. 12.
13. 14.
15.
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
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.
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87654321
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.
99 9 987654321
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87654321
0 0 0
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.
99 9 987654321
87654321
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87654321
0 0 0
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.
99 9 987654321
87654321
87654321
87654321
16. Find the length of X�Z� if Y(�4, 4) is the midpoint of X�Z� and X has coordinates (2, �4). (Lesson 1-3)
17. Find the perimeter of this hexagon.(Lesson 1-6)
18. Find the measure of W�X�, if the perimeter of pentagon UVWXY is 48 units. (Lesson 1-6)
10 � a
2aW X
U
V Y
4a � 7
30 m
20 m
7 m 6 m
10 m8.5 m
16.
17.
18.
2 8 . 9
1 1
5 5
2 0
11
Standardized Test PracticeStudent Record Sheet (Use with pages 58–59 of the Student Edition.)
11
© Glencoe/McGraw-Hill A1 Glencoe Geometry
An
swer
s
Select the best answer from the choices given and fill in the corresponding oval.
1 4 7
2 5 8
3 6 9 DCBADCBADCBA
DCBADCBADCBA
DCBADCBADCBA
NAME DATE PERIOD
Part 1 Multiple ChoicePart 1 Multiple Choice
Part 2 Short Response/Grid InPart 2 Short Response/Grid In
Part 3 Open-EndedPart 3 Open-Ended
Solve the problem and write your answer in the blank.
For Questions 14 and 15, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.
10 14 15
11
12
13
14 (grid in)
15 (grid in)
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
Record your answers for Questions 16–17 on the back of this paper.
© Glencoe/McGraw-Hill A2 Glencoe Geometry
Stu
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Po
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nes
ap
pea
r in
th
e fi
gure
?
Th
ere
are
thre
e pl
anes
:pla
ne
N,p
lan
e O
,an
d pl
ane
P.
b.
Are
poi
nts
A,B
,an
d D
cop
lan
ar?
Yes.
Th
ey a
re c
onta
ined
in
pla
ne
O.
Ref
er t
o th
e fi
gure
.
1.N
ame
a li
ne
that
is
not
con
tain
ed i
n p
lan
e N
.A
B��
�
2.N
ame
a pl
ane
that
con
tain
s po
int
B.
pla
ne
N,p
lan
e A
BC
,pla
ne
AB
D,p
lan
e E
BC
,p
lan
e E
BD
3.N
ame
thre
e co
llin
ear
poin
ts.
A,B
,E
Ref
er t
o th
e fi
gure
.
4.H
ow m
any
plan
es a
re s
how
n i
n t
he
figu
re?
6
5.A
re p
oin
ts B
,E,G
,an
d H
copl
anar
? E
xpla
in.
No
;B
,G,a
nd
Hlie
in p
lan
e B
GH
,bu
t E
do
es n
ot.
6.N
ame
a po
int
copl
anar
wit
h D
,C,a
nd
E.
Fo
r J
Dra
w a
nd
lab
el a
fig
ure
for
eac
h r
elat
ion
ship
.
7.P
lan
es M
andN
inte
rsec
t in
HJ
��� .
8.L
ine
ris
in
pla
ne
N,l
ine
sis
in
pla
ne
M,a
nd
lin
es r
and
sin
ters
ect
at p
oin
t J
.
9.L
ine
tco
nta
ins
poin
t H
and
lin
e td
oes
not
lie
in
pla
ne
Mor
plan
e N
.A
nsw
ers
for
Exe
rcis
es 7
–9
N
Ms
t
r
HJ
AB C
D
EFG
HI
J
N
A
C
B
D
E
NO
P
AB
CD
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Po
ints
,Lin
es,a
nd
Pla
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-1
1-1
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 1-1)
© Glencoe/McGraw-Hill A3 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Po
ints
,Lin
es,a
nd
Pla
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-1
1-1
©G
lenc
oe/M
cGra
w-H
ill3
Gle
ncoe
Geo
met
ry
Lesson 1-1
Ref
er t
o th
e fi
gure
.
1.N
ame
a li
ne
that
con
tain
s po
int
D.
po
r C
D��
�
2.N
ame
a po
int
con
tain
ed i
n l
ine
n.A
or
B
3.W
hat
is
anot
her
nam
e fo
r li
ne
p?C
D��
�o
r D
C��
�
4.N
ame
the
plan
e co
nta
inin
g li
nes
nan
d p.
Sam
ple
an
swer
:p
lan
e G
Dra
w a
nd
lab
el a
fig
ure
for
eac
h r
elat
ion
ship
.S
amp
le a
nsw
ers
are
giv
en.
5.P
oin
t K
lies
on
RT
��� .
6.P
lan
e J
con
tain
s li
ne
s.
7.Y
P� �
�li
es i
n p
lan
e B
and
con
tain
s 8.
Lin
es q
and
fin
ters
ect
at p
oin
t Z
poin
t C
,bu
t do
es n
ot c
onta
in p
oin
t H
.in
pla
ne
U.
Ref
er t
o th
e fi
gure
.
9.H
ow m
any
plan
es a
re s
how
n i
n t
he
figu
re?
5
10.H
ow m
any
of t
he
plan
es c
onta
in p
oin
ts F
and
E?
2
11.N
ame
fou
r po
ints
th
at a
re c
opla
nar
.
A,B
,E,F
or
B,C
,D,E
or
A,C
,D,F
12.A
re p
oin
ts A
,B,a
nd
Cco
plan
ar?
Exp
lain
.
Yes;
po
ints
A,B
,an
d C
lie in
pla
ne
W.
WA
BE
CDF
U
qf
Z
HP
B
CY
J
sT
RK
Gn
AB
D
C
p
©G
lenc
oe/M
cGra
w-H
ill4
Gle
ncoe
Geo
met
ry
Ref
er t
o th
e fi
gure
.
1.N
ame
a li
ne
that
con
tain
s po
ints
Tan
d P
.
g,T
P��
� ,T
N��
� ,N
P��
�
2.N
ame
a li
ne
that
in
ters
ects
th
e pl
ane
con
tain
ing
poin
ts Q
,N,a
nd
P.
jor
MT
���
3.N
ame
the
plan
e th
at c
onta
ins
TN
���
and
QR
��� .
Sam
ple
an
swer
:p
lan
e S
Dra
w a
nd
lab
el a
fig
ure
for
eac
h r
elat
ion
ship
.S
amp
le a
nsw
ers
are
giv
en.
4.A
K��
�an
d C
G��
�in
ters
ect
at p
oin
t M
5.A
line
con
tain
s L
(�4,
�4)
and
M(2
,3).
Lin
e in
pla
ne
T.q
is i
n t
he
sam
e co
ordi
nat
e pl
ane
but
does
not
in
ters
ect
LM
� �� .
Lin
e q
con
tain
s po
int
N.
Ref
er t
o th
e fi
gure
.
6.H
ow m
any
plan
es a
re s
how
n i
n t
he
figu
re?
6
7.N
ame
thre
e co
llin
ear
poin
ts.
S,X
,M
8.A
re p
oin
ts N
,R,S
,an
d W
copl
anar
? E
xpla
in.
No
;sa
mp
le a
nsw
er:
po
ints
N,R
,an
d S
lie
in p
lan
e A
,bu
t p
oin
t W
do
es n
ot.
VIS
UA
LIZA
TIO
NN
ame
the
geom
etri
c te
rm(s
) m
odel
ed b
y ea
ch o
bje
ct.
9.10
.11
.
pla
ne
and
lin
ep
oin
tlin
es
12.a
car
an
ten
na
13.a
lib
rary
car
dlin
e an
d p
oin
tp
lan
e
strin
gs
tip o
f pin
STOP
AM
N
PW
S XRQ
T
L
M
N
q
x
y
O
KT
M
C
GA
S
j
ghTM
NQ
R
P
Pra
ctic
e (
Ave
rag
e)
Po
ints
,Lin
es,a
nd
Pla
nes
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-1
1-1
Answers (Lesson 1-1)
© Glencoe/McGraw-Hill A4 Glencoe Geometry
Readin
g t
o L
earn
Math
em
ati
csP
oin
ts,L
ines
,an
d P
lan
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-1
1-1
©G
lenc
oe/M
cGra
w-H
ill5
Gle
ncoe
Geo
met
ry
Lesson 1-1
Pre-
Act
ivit
yW
hy
do
chai
rs s
omet
imes
wob
ble
?
Rea
d th
e in
trod
uct
ion
to
Les
son
1-1
at
the
top
of p
age
6 in
you
r te
xtbo
ok.
•F
ind
thre
e pe
nci
ls o
f di
ffer
ent
len
gth
s an
d h
old
them
upr
igh
t on
you
rde
sk s
o th
at t
he
thre
e pe
nci
l po
ints
do
not
lie
alo
ng
a si
ngl
e li
ne.
Can
you
plac
e a
flat
sh
eet
of p
aper
or
card
boar
d so
th
at i
t to
uch
es a
ll t
hre
e pe
nci
lpo
ints
?ye
s•
How
man
y w
ays
can
you
do
this
if
you
kee
p th
e pe
nci
l po
ints
in
th
e sa
me
posi
tion
?o
ne
•H
ow w
ill
you
r an
swer
ch
ange
if
ther
e ar
e fo
ur
pen
cil
poin
ts?
Sam
ple
answ
er:
It m
ay n
ot
be
po
ssib
le t
o p
lace
th
e p
aper
to
to
uch
all f
ou
r p
oin
ts.
Rea
din
g t
he
Less
on
1.C
ompl
ete
each
sen
ten
ce.
a.P
oin
ts t
hat
lie
on
th
e sa
me
lie
are
call
ed
poin
ts.
b.
Poi
nts
th
at d
o n
ot l
ie i
n t
he
sam
e pl
ane
are
call
ed
poin
ts.
c.T
her
e is
exa
ctly
on
e th
rou
gh a
ny
two
poin
ts.
d.
Th
ere
is e
xact
ly o
ne
thro
ugh
an
y th
ree
non
coll
inea
r po
ints
.
2.R
efer
to
the
figu
re a
t th
e ri
ght.
Indi
cate
wh
eth
er e
ach
st
atem
ent
is t
rue
or f
alse
.
a.P
oin
ts A
,B,a
nd
Car
e co
llin
ear.
fals
e
b.
Th
e in
ters
ecti
on o
f pl
ane
AB
Can
d li
ne
mis
poi
nt
P.
tru
e
c.L
ine
�an
d li
ne
mdo
not
in
ters
ect.
fals
e
d.
Poi
nts
A,P
,an
d B
can
be
use
d to
nam
e pl
ane
U.
fals
e
e.L
ine
�li
es i
n p
lan
e A
CB
.tr
ue
3.C
ompl
ete
the
figu
re a
t th
e ri
ght
to s
how
th
e fo
llow
ing
rela
tion
ship
:Lin
es �
,m,a
nd
nar
e co
plan
ar a
nd
lie
in
plan
e Q
.Lin
es �
and
min
ters
ect
at p
oin
t P
.Lin
e n
inte
rsec
ts l
ine
mat
R,b
ut
does
not
in
ters
ect
lin
e �.
Hel
pin
g Y
ou
Rem
emb
er
4.R
ecal
l or
loo
k in
a d
icti
onar
y to
fin
d th
e m
ean
ing
of t
he
pref
ix c
o-.W
hat
doe
s th
is p
refi
xm
ean
? H
ow c
an i
t h
elp
you
rem
embe
r th
e m
ean
ing
of c
olli
nea
r?S
amp
le a
nsw
er:T
he
pre
fix
co-
mea
ns
tog
eth
er.T
he
wo
rd c
olli
nea
rco
nta
ins
the
wo
rd li
ne,
so c
olli
nea
rm
ean
s to
get
her
on
a li
ne.
Qn
m
�P
R
U
m
�P
C
D
B
A
pla
ne
line
no
nco
pla
nar
colli
nea
r
©G
lenc
oe/M
cGra
w-H
ill6
Gle
ncoe
Geo
met
ry
Po
ints
an
d L
ines
on
a M
atri
xA
mat
rix
is a
rec
tan
gula
r ar
ray
of r
ows
and
colu
mn
s.P
oin
ts a
nd
lin
es o
n a
mat
rix
are
not
def
ined
in
th
e sa
me
way
as
in E
ucl
idea
nge
omet
ry.A
poi
nt
on a
mat
rix
is a
dot
,wh
ich
can
be
smal
l or
larg
e.A
lin
e on
a m
atri
x is
a p
ath
of
dots
th
at “
lin
e u
p.”
Bet
wee
ntw
o po
ints
on
a l
ine
ther
e m
ay o
r m
ay n
ot b
e ot
her
poi
nts
.Th
ree
exam
ples
of
lin
es a
re s
how
n a
t th
e u
pper
rig
ht.
Th
e br
oad
lin
e ca
nbe
th
ough
t of
as
a si
ngl
e li
ne
or a
s tw
o n
arro
w l
ines
sid
e by
sid
e.
Dot
-mat
rix
prin
ters
for
com
pute
rs u
sed
dots
to
form
ch
arac
ters
.T
he
dots
are
oft
en c
alle
d p
ixel
s.T
he
mat
rix
at t
he
righ
t sh
ows
how
a d
ot-m
atri
x pr
inte
r m
igh
t pr
int
the
lett
er P
.
An
swer
s m
ay v
ary.
Sam
ple
an
swer
s ar
e sh
ow
n.
Dra
w p
oin
ts o
n e
ach
mat
rix
to c
reat
e th
e gi
ven
fig
ure
s.
1.D
raw
tw
o in
ters
ecti
ng
lin
es t
hat
hav
e2.
Dra
w t
wo
lin
es t
hat
cro
ss b
ut
hav
e fo
ur
poin
ts i
n c
omm
on.
no
com
mon
poi
nts
.
3.M
ake
the
nu
mbe
r 0
(zer
o) s
o th
at i
t4.
Mak
e th
e ca
pita
l le
tter
O s
o th
at i
tex
ten
ds t
o th
e to
p an
d bo
ttom
sid
esex
ten
ds t
o ea
ch s
ide
of t
he
mat
rix.
of t
he
mat
rix.
5.U
sin
g se
para
te g
rid
pape
r,m
ake
dot
desi
gns
for
seve
ral
oth
er l
ette
rs.W
hic
h w
ere
the
easi
est
and
wh
ich
wer
e th
e m
ost
diff
icu
lt?
See
stu
den
ts’w
ork
.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-1
1-1
Answers (Lesson 1-1)
© Glencoe/McGraw-Hill A5 Glencoe Geometry
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Lin
ear
Mea
sure
an
d P
reci
sio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
1-2
©G
lenc
oe/M
cGra
w-H
ill7
Gle
ncoe
Geo
met
ry
Lesson 1-2
Mea
sure
Lin
e Se
gm
ents
A p
art
of a
lin
e be
twee
n t
wo
endp
oin
ts i
s ca
lled
a l
ine
segm
ent.
Th
e le
ngt
hs
of M �
N�an
d R�
S�ar
e w
ritt
en a
s M
Nan
d R
S.W
hen
you
mea
sure
ase
gmen
t,th
e pr
ecis
ion
of
the
mea
sure
men
t is
hal
f of
th
e sm
alle
st u
nit
on
th
e ru
ler.
Fin
d t
he
len
gth
of
M�N�
.
Th
e lo
ng
mar
ks a
re c
enti
met
ers,
and
the
shor
ter
mar
ks a
re m
illi
met
ers.
Th
e le
ngt
h o
f M �
N�is
3.4
cen
tim
eter
s.T
he
mea
sure
men
t is
ac
cura
te t
o w
ith
in 0
.5 m
illi
met
er,s
o M �
N�is
betw
een
3.3
5 ce
nti
met
ers
and
3.45
cen
tim
eter
s lo
ng.
1cm
23
4
MN
Fin
d t
he
len
gth
of
R�S�
.
Th
e lo
ng
mar
ks a
re i
nch
es a
nd
the
shor
t m
arks
are
qu
arte
r in
ches
.Th
e le
ngt
h o
f R �
S�is
abo
ut
1�3 4�
inch
es.T
he
mea
sure
men
t is
accu
rate
to
wit
hin
one
half
of
a qu
arte
r in
ch,
or �1 8�
inch
,so
R�S�
is b
etw
een
1�5 8�
inch
es a
nd
1�7 8�
inch
es l
ong.1
2in
.
RS
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d t
he
len
gth
of
each
lin
e se
gmen
t or
ob
ject
.
1.2.
5 cm
2.1�
1 4�in
.
3.2�
1 4�in
.4.
1.7
cm
Fin
d t
he
pre
cisi
on f
or e
ach
mea
sure
men
t.
5.10
in
.6.
32 m
m7.
44 c
m
�1 2�in
.0.
5 m
m0.
5 cm
8.2
ft9.
3.5
mm
10.2
�1 2�yd
�1 2�ft
or
6 in
.0.
05 m
m�1 4�
yd o
r 9
in.
1cm
23
12
in.
1in
.
ST
1cm
23
AB
©G
lenc
oe/M
cGra
w-H
ill8
Gle
ncoe
Geo
met
ry
Cal
cula
te M
easu
res
On
PQ
��� ,
to s
ay t
hat
poi
nt
Mis
be
twee
n p
oin
ts P
and
Qm
ean
s P,
Q,a
nd
Mar
e co
llin
ear
and
PM
�M
Q�
PQ
.
On
AC
��� ,
AB
�B
C�
3 cm
.We
can
say
th
at t
he
segm
ents
are
con
gru
ent,
or A �
B��
B�C�
.Sla
shes
on
th
e fi
gure
in
dica
te w
hic
hse
gmen
ts a
re c
ongr
uen
t.
AB
C
QM
P
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Lin
ear
Mea
sure
an
d P
reci
sio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
1-2
Fin
d E
F.
Cal
cula
te E
Fby
add
ing
ED
and
DF
.
ED
�D
F�
EF
1.2
�1.
9 �
EF
3.1
�E
F
Th
eref
ore,
E �F�
is 3
.1 c
enti
met
ers
lon
g.
E1.
2 cm
1.9
cm
FD
Fin
d x
and
AC
.
Bis
bet
wee
n A
and
C.
AB
�B
C�
AC
x�
2x�
2x�
53x
�2x
�5
x�
5A
C�
2x�
5 �
2(5)
�5
�15
Ax
2xC
B
2x �
5
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d t
he
mea
sure
men
t of
eac
h s
egm
ent.
Ass
um
e th
at t
he
art
is n
ot d
raw
n t
o sc
ale.
1.R�
T�4.
5 cm
2.B�
C�3
�1 4�in
.
3.X�
Z�4
�1 4�in
.4.
W�X�
3 cm
Fin
d x
and
RS
if S
is b
etw
een
Ran
d T
.
5.R
S�
5x,S
T�
3x,a
nd
RT
�48
.6,
306.
RS
�2x
,ST
�5x
�4,
and
RT
�32
.4,
8
7.R
S�
6x,S
T�
12,a
nd
RT
�72
.10
,60
8.R
S�
4x,R�
S��
S�T�
,an
d R
T�
24.
3,12
Use
th
e fi
gure
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
seg
men
ts i
s co
ngr
uen
t.
9.A �
B�an
d C�
D�ye
s10
.X�Y�
and
Y�Z�
no
X
YZ
3x �
55x
� 1
9x 2
AD
CB
11 c
m
11 c
m
5 cm
5 cm
WY
6 cm X
XZ
Y
3 – 4 in.
31 – 2 in.
AC
6 in
.
23 – 4 in.
BR
T
2.0
cm2.
5 cm
S
Answers (Lesson 1-2)
© Glencoe/McGraw-Hill A6 Glencoe Geometry
Skil
ls P
ract
ice
Lin
ear
Mea
sure
an
d P
reci
sio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
1-2
©G
lenc
oe/M
cGra
w-H
ill9
Gle
ncoe
Geo
met
ry
Lesson 1-2
Fin
d t
he
len
gth
of
each
lin
e se
gmen
t or
ob
ject
.
1.2.
abo
ut
55 m
mab
ou
t 2�
1 4�in
.
Fin
d t
he
pre
cisi
on f
or e
ach
mea
sure
men
t.
3.40
fee
t4.
12 c
enti
met
ers
5.9�
1 2�in
ches
0.5
ft0.
5 cm
�1 4�in
.
Fin
d t
he
mea
sure
men
t of
eac
h s
egm
ent.
6.N�
Q�7.
A�C�
8.G�
H�
2�1 4�
in.
10.1
cm
5.3
mm
Fin
d t
he
valu
e of
th
e va
riab
le a
nd
YZ
if Y
is b
etw
een
Xan
d Z
.
9.X
Y�
5p,Y
Z�
p,an
d X
Y�
2510
.XY
�12
,YZ
�2g
,an
d X
Z�
28
5;5
8;16
11.X
Y�
4m,Y
Z�
3m,a
nd
XZ
�42
12.X
Y�
2c�
1,Y
Z�
6c,a
nd
XZ
�81
6;18
10;
60
Use
th
e fi
gure
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
seg
men
ts i
s co
ngr
uen
t.
13.B�
E�,C�
D�14
.M�P�
,N�P�
15.W�
X�,W�
Z�
yes
no
noY
Z
WX
9 ft
5 ft
5 ft
NP
M10
yd
12 y
d
12 y
dE
D
CB
5 m
2 m
3 m
3 m
F9.
7 m
mH
G
15 m
mA
4.9
cm5.
2 cm
CB
Q1i
n.11 – 4 in
.
NP
12
in.
1cm
23
54
©G
lenc
oe/M
cGra
w-H
ill10
Gle
ncoe
Geo
met
ry
Fin
d t
he
len
gth
of
each
lin
e se
gmen
t or
ob
ject
.
1.2.
1�1 11 6�
in.
42 m
m
Fin
d t
he
pre
cisi
on f
or e
ach
mea
sure
men
t.
3.12
0 m
eter
s4.
7�1 4�
inch
es5.
30.0
mil
lim
eter
s
0.5
m�1 8�
in.
0.5
mm
Fin
d t
he
mea
sure
men
t of
eac
h s
egm
ent.
6.P�
S�7.
A�D�
8.W�
X�
23.1
cm
3�5 8�
in.
10.4
cm
Fin
d t
he
valu
e of
th
e va
riab
le a
nd
KL
if K
is b
etw
een
Jan
d L
.
9.J
K�
6r,K
L�
3r,a
nd
JL
�27
10.J
K�
2s,K
L�
s�
2,an
d J
L�
5s�
10
3;9
6;8
Use
th
e fi
gure
s to
det
erm
ine
wh
eth
er e
ach
pai
r of
seg
men
ts i
s co
ngr
uen
t.
11.T�
U�,S�
W�12
.A�D�
,B�C�
13.G�
F�,F�
E�
no
yes
no
14.C
AR
PEN
TRY
Jorg
e u
sed
the
figu
re a
t th
e ri
ght
to m
ake
a pa
tter
n
for
a m
osai
c h
e pl
ans
to i
nla
y on
a t
able
top.
Nam
e al
l of
th
e co
ngr
uen
t se
gmen
ts i
n t
he
figu
re.
B�C�
�F�E�
,A�B�
�C�
D��
D�E�
�F�A�
DA
BF E
C
GH
EF5x
6xD
C
BA
12.9
in.
12.7
in.
W
TS
U
2 ft
2 ft
3 ft
3 ft
W89
.6 c
mY
X
100
cmA
11 – 4 in.
23 – 8 in.
DC
P4.
7 cm
18.4
cm
SQ
1cm
23
54
12
in.
EF
Pra
ctic
e (
Ave
rag
e)
Lin
ear
Mea
sure
an
d P
reci
sio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
1-2
Answers (Lesson 1-2)
© Glencoe/McGraw-Hill A7 Glencoe Geometry
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csL
inea
r M
easu
re a
nd
Pre
cisi
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
1-2
©G
lenc
oe/M
cGra
w-H
ill11
Gle
ncoe
Geo
met
ry
Lesson 1-2
Pre-
Act
ivit
yW
hy
are
un
its
of m
easu
re i
mp
orta
nt?
Rea
d th
e in
trod
uct
ion
to
Les
son
1-2
at
the
top
of p
age
13 i
n y
our
text
book
.
•T
he
basi
c u
nit
of
len
gth
in
th
e m
etri
c sy
stem
is
the
met
er.H
ow m
any
met
ers
are
ther
e in
on
e ki
lom
eter
?10
00•
Do
you
th
ink
it w
ould
be
easi
er t
o le
arn
th
e re
lati
onsh
ips
betw
een
th
edi
ffer
ent
un
its
of l
engt
h i
n t
he
cust
omar
y sy
stem
(u
sed
in t
he
Un
ited
Sta
tes)
or
in t
he m
etri
c sy
stem
? E
xpla
in y
our
answ
er.
Sam
ple
an
swer
:T
he
met
ric
syst
em is
eas
ier
bec
ause
yo
u c
an c
han
ge
bet
wee
n t
he
dif
fere
nt
un
its
by ju
st m
ovin
g t
he
dec
imal
po
int.
Rea
din
g t
he
Less
on
1.E
xpla
in t
he
diff
eren
ce b
etw
een
a l
ine
and
a li
ne
segm
ent
and
wh
y on
e of
th
ese
can
be
mea
sure
d,w
hil
e th
e ot
her
can
not
.S
amp
le a
nsw
er:
A li
ne
is in
fin
ite.
Sin
ce it
has
no
en
dp
oin
ts,a
lin
e d
oes
no
t h
ave
a d
efin
ite
len
gth
an
d c
ann
ot
be
mea
sure
d.A
lin
e se
gm
ent
has
two
en
dp
oin
ts,s
o it
has
a d
efin
ite
len
gth
an
d c
an b
e m
easu
red
.
2.W
hat
is
the
smal
lest
len
gth
mar
ked
on a
12-
inch
ru
ler?
Sam
ple
an
swer
:� 11 6�
in.
Wh
at i
s th
e sm
alle
st l
engt
h m
arke
d on
a c
enti
met
er r
ule
r?1
mm
3.F
ind
the
prec
isio
n o
f ea
ch m
easu
rem
ent.
a.15
cm
0.5
cmb
.15
.0 c
m0.
05 c
m
4.R
efer
to
the
figu
re a
t th
e ri
ght.
Wh
ich
on
e of
th
e fo
llow
ing
stat
emen
ts i
s tr
ue?
Exp
lain
you
r an
swer
.A �
B��
C�D�
A�B�
�C �
D�
A�B�
�C�
D�;
Sam
ple
an
swer
:Th
e tw
o s
egm
ents
are
co
ng
ruen
t b
ecau
se t
hey
hav
e th
e sa
me
mea
sure
or
len
gth
.Th
ey a
re n
ot
equ
al b
ecau
se t
hey
are
no
t th
e sa
me
seg
men
t.
5.S
upp
ose
that
Sis
a p
oin
t on
V�W�
and
Sis
not
th
e sa
me
poin
t as
Vor
W.T
ell
wh
eth
erea
ch o
f th
e fo
llow
ing
stat
emen
ts i
s al
way
s,so
met
imes
,or
nev
ertr
ue.
a.V
S�
SW
som
etim
esb
.S
is b
etw
een
Van
d W
.al
way
sc.
VS
�V
W�
SW
nev
er
Hel
pin
g Y
ou
Rem
emb
er
6.A
goo
d w
ay t
o re
mem
ber
term
s u
sed
in m
ath
emat
ics
is t
o re
late
th
em t
o ev
eryd
ay w
ords
you
kn
ow.G
ive
thre
e w
ords
th
at a
re u
sed
outs
ide
of m
ath
emat
ics
that
can
hel
p yo
ure
mem
ber
that
th
ere
are
100
cen
tim
eter
s in
a m
eter
.S
amp
le a
nsw
er:
cen
t,ce
ntu
ry,c
ente
nn
ial
A
B
4.5
cm4.
5 cm
DC
©G
lenc
oe/M
cGra
w-H
ill12
Gle
ncoe
Geo
met
ry
Po
ints
Eq
uid
ista
nt
fro
m S
egm
ents
Th
e di
stan
ce f
rom
a p
oin
t to
a s
egm
ent
is z
ero
if t
he
poin
t is
on
th
e se
gmen
t.O
ther
wis
e,it
is
the
len
gth
of
the
shor
test
seg
men
t fr
om t
he
poin
t to
th
e se
gmen
t.
A f
igu
re i
s a
locu
sif
it
is t
he
set
of a
ll p
oin
ts t
hat
sat
isfy
a se
t of
con
diti
ons.
Th
e lo
cus
of a
ll p
oin
ts t
hat
are
�1 4�in
ch
from
th
e se
gmen
t A
Bis
sh
own
by
two
dash
ed s
egm
ents
w
ith
sem
icir
cles
at
both
en
ds.
1.S
upp
ose
A,B
,C,a
nd
Dar
e fo
ur
diff
eren
t po
ints
,an
d co
nsi
der
the
locu
s of
all
poi
nts
xu
nit
s fr
om A�
B�an
dx
un
its
from
C�D�
.Use
an
y u
nit
you
fin
dco
nve
nie
nt.
Th
e lo
cus
can
tak
e di
ffer
ent
form
s.S
ketc
h a
t le
ast
thre
epo
ssib
ilit
ies.
Lis
t so
me
of t
he
thin
gs t
hat
see
m t
o af
fect
th
e fo
rm o
f th
e lo
cus.
Sam
ple
an
swer
s ar
e sh
ow
n.
Th
e lo
cus
is 1
Th
e lo
cus
is a
set
of
Th
e lo
cus
is a
pai
r se
gm
ent
X�Y�
mid
way
2 p
oin
ts,X
and
Y.
of
line
seg
men
ts,
bet
wee
n A�
B�an
d C�
D�.
R�S�
and
P�Q�
.
Th
e lo
cus
of
po
ints
xu
nit
s fr
om
A�B�
and
C�D�
dep
end
s o
n t
he
dis
tan
ce x
and
ho
w A�
B�an
d C�
D�ar
e si
tuat
ed r
elat
ive
to o
ne
ano
ther
.
2.C
ondu
ct y
our
own
in
vest
igat
ion
of
the
locu
s of
poi
nts
equ
idis
tan
tfr
om t
wo
segm
ents
.Des
crib
e yo
ur
resu
lts
on a
sepa
rate
sh
eet
of p
aper
.S
ee s
tud
ents
’wo
rk.
AB
CD
PQ
RS
A
B
C
D
X
Y
AB
CD
XY
AB
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
1-2
Answers (Lesson 1-2)
© Glencoe/McGraw-Hill A8 Glencoe Geometry
Stu
dy G
uid
e a
nd I
nte
rven
tion
Dis
tan
ce a
nd
Mid
po
ints
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
1-3
©G
lenc
oe/M
cGra
w-H
ill13
Gle
ncoe
Geo
met
ry
Lesson 1-3
Dis
tan
ce B
etw
een
Tw
o P
oin
ts
Dis
tan
ce o
n a
Nu
mb
er L
ine
Dis
tan
ce in
th
e C
oo
rdin
ate
Pla
ne
AB
�|b
�a
|or
|a�
b|
x
y
OC
( 1, –
1)A
( –2,
–1)
B( 1
, 3)
Pyt
hago
rean
The
orem
:
a2�
b2�
c2
Dis
tanc
e F
orm
ula:
d�
�(x
2�
�x 1
)2�
�(y
2�
�y 1
)2�
AB
ab
Fin
d A
B.
AB
�|(�
4) �
2|�
|�6|
�6
�5
�4
�3
�2
�1
01
23
AB
Fin
d t
he
dis
tan
ce b
etw
een
A
(�2,
�1)
an
d B
(1,3
).
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Pyt
hag
orea
n T
heo
rem
(AB
)2�
(AC
)2�
(BC
)2
(AB
)2�
(3)2
�(4
)2
(AB
)2�
25
AB
��
25��
5
Dis
tan
ce F
orm
ula
d�
�(x
2�
�x 1
)2�
�(y
2�
�y 1
)2�
AB
��
(1 �
(�
�2)
)2�
�(3
��
(�1)
)�
2 �A
B�
�(3
)2�
�(4
)2�
��
25��
5
Use
th
e n
um
ber
lin
e to
fin
d e
ach
mea
sure
.
1.B
D6
2.D
G9
3.A
F12
4.E
F3
5.B
G15
6.A
G17
7.B
E7
8.D
E1
Use
th
e P
yth
agor
ean
Th
eore
m t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
9.A
(0,0
),B
(6,8
)10
10.R
(�2,
3),S
(3,1
5)13
11.M
(1,�
2),N
(9,1
3)17
12.E
(�12
,2),
F(�
9,6)
5
Use
th
e D
ista
nce
For
mu
la t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
13.A
(0,0
),B
(15,
20)
2514
.O(�
12,0
),P
(�8,
3)5
15.C
(11,
�12
),D
(6,2
)�
221
��
14.9
16.E
(�2,
10),
F(�
4,3)
�53�
�7.
3
–10
–8–6
–4–2
02
46
8
AB
CD
EF
G
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill14
Gle
ncoe
Geo
met
ry
Mid
po
int
of
a Se
gm
ent
Mid
po
int
on
aIf
the
coor
dina
tes
of t
he e
ndpo
ints
of
a se
gmen
t ar
e a
and
b,
Nu
mb
er L
ine
then
the
coo
rdin
ate
of t
he m
idpo
int
of t
he s
egm
ent
is �a
� 2b
�.
Mid
po
int
on
aIf
a se
gmen
t ha
s en
dpoi
nts
with
coo
rdin
ates
(x 1
, y 1
) an
d (x
2, y
2),
Co
ord
inat
e P
lan
eth
en t
he c
oord
inat
es o
f th
e m
idpo
int
of t
he s
egm
ent
are
��x 1� 2
x 2�
, �y 1
� 2y 2
��.
Fin
d t
he
coor
din
ate
of t
he
mid
poi
nt
of P�
Q�.
Th
e co
ordi
nat
es o
f P
and
Qar
e �
3 an
d 1.
If M
is t
he
mid
poin
t of
P�Q�
,th
en t
he
coor
din
ate
of M
is ��
3 2�1
��
�� 22 �or
�1.
Mis
th
e m
idp
oin
t of
P �Q�
for
P(�
2,4)
an
d Q
(4,1
).F
ind
th
eco
ord
inat
es o
f M
.
M�
��x 1� 2
x 2�
,�y 1
� 2y 2
���
���2 2�
4�
,�4
� 21
��o
r (1
,2.5
)
Use
th
e n
um
ber
lin
e to
fin
d t
he
coor
din
ate
of
the
mid
poi
nt
of e
ach
seg
men
t.
1.C �
E��
12.
D�G�
4
3.A�
F��
34.
E�G�
5
5.A�
B��
86.
B�G�
�1 2�
7.B�
D��
3�1 2�
8.D�
E�1
Fin
d t
he
coor
din
ates
of
the
mid
poi
nt
of a
seg
men
t h
avin
g th
e gi
ven
en
dp
oin
ts.
9.A
(0,0
),B
(12,
8)(6
,4)
10.R
(�12
,8),
S(6
,12)
(�3,
10)
11.M
(11,
�2)
,N(�
9,13
)(1
,5.5
)12
.E(�
2,6)
,F(�
9,3)
(�5.
5,4.
5)
13.S
(10,
�22
),T
(9,1
0)(9
.5,�
6)14
.M(�
11,2
),N
(�19
,6)
(�15
,4)
–10
–8–6
–4–2
02
46
8
AB
CD
EF
G
–3–2
–10
12
PQ
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Dis
tan
ce a
nd
Mid
po
ints
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
1-3
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Answers (Lesson 1-3)
© Glencoe/McGraw-Hill A9 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Dis
tan
ce a
nd
Mid
po
ints
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
1-3
©G
lenc
oe/M
cGra
w-H
ill15
Gle
ncoe
Geo
met
ry
Lesson 1-3
Use
th
e n
um
ber
lin
e to
fin
d e
ach
mea
sure
.
1.L
N6
2.J
L8
3.K
N11
4.M
N3
Use
th
e P
yth
agor
ean
Th
eore
m t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
5.5
6.10
7.K
(2,3
),F
(4,4
)8.
C(�
3,�
1),Q
(�2,
3)
�5�
�2.
2�
17��
4.1
Use
th
e D
ista
nce
For
mu
la t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
9.Y
(2,0
),P
(2,6
)10
.W(�
2,2)
,R(5
,2)
67
11.A
(�7,
�3)
,B(5
,2)
12.C
(�3,
1),Q
(2,6
)
13�
50��
7.1
Use
th
e n
um
ber
lin
e to
fin
d t
he
coor
din
ate
of t
he
mid
poi
nt
of e
ach
seg
men
t.
13.D �
E�9
14.B�
C�1
15.B�
D�3
16.A�
D�1�
1 2�
Fin
d t
he
coor
din
ates
of
the
mid
poi
nt
of a
seg
men
t h
avin
g th
e gi
ven
en
dp
oin
ts.
17.T
(3,1
),U
(5,3
)18
.J(�
4,2)
,F(5
,�2)
(4,2
)��1 2� ,
0 �F
ind
th
e co
ord
inat
es o
f th
e m
issi
ng
end
poi
nt
give
n t
hat
Pis
th
e m
idp
oin
t of
N�Q�
.
19.N
(2,0
),P
(5,2
)20
.N(5
,4),
P(6
,3)
21.Q
(3,9
),P
(�1,
5)
Q(8
,4)
Q(7
,2)
N(�
5,1)
–6–4
–20
24
68
1012
AB
CD
E
x
y
O
D
S
x
y
O
F
G
–6–4
–20
24
68
10
JK
LM
N
©G
lenc
oe/M
cGra
w-H
ill16
Gle
ncoe
Geo
met
ry
Use
th
e n
um
ber
lin
e to
fin
d e
ach
mea
sure
.
1.V
W4
2.T
V5
3.S
T3
4.S
V8
Use
th
e P
yth
agor
ean
Th
eore
m t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
5.6.
�65�
�8.
1�
113
��
10.6
Use
th
e D
ista
nce
For
mu
la t
o fi
nd
th
e d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
7.L
(�7,
0),Y
(5,9
)8.
U(1
,3),
B(4
,6)
15�
18��
4.2
Use
th
e n
um
ber
lin
e to
fin
d t
he
coor
din
ate
of t
he
mid
poi
nt
of e
ach
seg
men
t.
9.R �
T�1
10.Q�
R��
4
11.S�
T�2�
1 2�12
.P�R�
�5
�1 2�
Fin
d t
he
coor
din
ates
of
the
mid
poi
nt
of a
seg
men
t h
avin
g th
e gi
ven
en
dp
oin
ts.
13.K
(�9,
3),H
(5,7
)14
.W(�
12,�
7),T
(�8,
�4)
(�2,
5)(�
10,�
5.5)
Fin
d t
he
coor
din
ates
of
the
mis
sin
g en
dp
oin
t gi
ven
th
at E
is t
he
mid
poi
nt
of D�
F�.
15.F
(5,8
),E
(4,3
)16
.F(2
,9),
E(�
1,6)
17.D
(�3,
�8)
,E(1
,�2)
D(3
,�2)
D(�
4,3)
F(5
,4)
18.P
ERIM
ETER
Th
e co
ordi
nat
es o
f th
e ve
rtic
es o
f a
quad
rila
tera
l ar
e R
(�1,
3),S
(3,3
),T
(5,�
1),a
nd
U(�
2,�
1).F
ind
the
peri
met
er o
f th
e qu
adri
late
ral.
Rou
nd
to t
he
nea
rest
ten
th.
19.6
un
its
–6–4
–10
–8–2
02
46
PQ
RS
T
x
y
O
E
S
x
y
OM
Z
–6–4
–10
–8–2
02
46
8
ST
UV
W
Pra
ctic
e (
Ave
rag
e)
Dis
tan
ce a
nd
Mid
po
ints
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
1-3
Answers (Lesson 1-3)
© Glencoe/McGraw-Hill A10 Glencoe Geometry
Readin
g t
o L
earn
Math
em
ati
csD
ista
nce
an
d M
idp
oin
ts
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
1-3
©G
lenc
oe/M
cGra
w-H
ill17
Gle
ncoe
Geo
met
ry
Lesson 1-3
Pre-
Act
ivit
yH
ow c
an y
ou f
ind
th
e d
ista
nce
bet
wee
n t
wo
poi
nts
wit
hou
t a
rule
r?
Rea
d th
e in
trod
uct
ion
to
Les
son
1-3
at
the
top
of p
age
21 i
n y
our
text
book
.
•L
ook
at t
he
tria
ngl
e in
th
e in
trod
uct
ion
to
this
les
son
.Wh
at i
s th
e sp
ecia
ln
ame
for
A�B�
in t
his
tri
angl
e?hy
po
ten
use
•F
ind
AB
in t
his
fig
ure
.Wri
te y
our
answ
er b
oth
as
a ra
dica
l an
d as
ade
cim
al n
um
ber
rou
nde
d to
th
e n
eare
st t
enth
.�
61�u
nit
s;7.
8 u
nit
s
Rea
din
g t
he
Less
on
1.M
atch
eac
h f
orm
ula
or
expr
essi
on i
n t
he
firs
t co
lum
n w
ith
on
e of
th
e n
ames
in
th
ese
con
d co
lum
n.
a.d
��
(x2
��
x 1)2
��
(y2
��
y 1)2
�ii
i.P
yth
agor
ean
Th
eore
m
b.
�a� 2
b�
vii
.Dis
tan
ce F
orm
ula
in
th
e C
oord
inat
e P
lan
e
c.X
Y�
| a�
b| i
vii
i.M
idpo
int
of a
Seg
men
t in
th
e C
oord
inat
e P
lan
e
d.
c2�
a2�
b2i
iv.
Dis
tan
ce F
orm
ula
on
a N
um
ber
Lin
e
e.��x 1
� 2x 2
�,�
y 1� 2
y 2�
�iii
v.M
idpo
int
of a
Seg
men
t on
a N
um
ber
Lin
e
2.F
ill
in t
he
step
s to
cal
cula
te t
he
dist
ance
bet
wee
n t
he
poin
ts M
(4,�
3) a
nd
N(�
2,7)
.
Let
(x 1
,y1)
�(4
,�3)
.Th
en (
x 2,y
2) �
(,
).
d�
��
��
�(
�)2
�(
�)2
MN
���
��
�(
�)2
�(
�)2
MN
���
�(
)2�
()2
MN
���
��
MN
���
Fin
d a
deci
mal
app
roxi
mat
ion
for
MN
to t
he
nea
rest
hu
ndr
edth
.11
.66
Hel
pin
g Y
ou
Rem
emb
er
3.A
goo
d w
ay t
o re
mem
ber
a n
ew f
orm
ula
in
mat
hem
atic
s is
to
rela
te i
t to
on
e yo
u a
lrea
dykn
ow.I
f yo
u f
orge
t th
e D
ista
nce
For
mu
la,h
ow c
an y
ou u
se t
he
Pyt
hag
orea
n T
heo
rem
to
fin
d th
e di
stan
ce d
betw
een
tw
o po
ints
on
a c
oord
inat
e pl
ane?
Sam
ple
an
swer
:If
th
ese
gm
ent
det
erm
ined
by
the
po
ints
is n
eith
er h
ori
zon
tal n
or
vert
ical
,dra
wa
rig
ht
tria
ng
le t
hat
has
th
e se
gm
ent
as it
s hy
po
ten
use
.Th
e h
ori
zon
tal
sid
e w
ill h
ave
len
gth
|x2
�x 1
|an
d t
he
vert
ical
sid
e w
ill h
ave
len
gth
|y 2
�y 1
|.By
the
Pyt
hag
ore
an T
heo
rem
,d2
�|x 2
�x 1
|2�
|y 2�
y 1|2
�
(x 2�
x 1)2
�(y 2
�y 1
)2 .
136
100
36
10�
6
�3
74
�2
y 1y 2
x 1x 2
7�
2
©G
lenc
oe/M
cGra
w-H
ill18
Gle
ncoe
Geo
met
ry
Len
gth
s o
n a
Gri
dE
ven
ly-s
pace
d h
oriz
onta
l an
d ve
rtic
al l
ines
for
m a
gri
d.
You
can
eas
ily
fin
d se
gmen
t le
ngt
hs
on
a gr
id i
f th
e en
dpoi
nts
are
gri
d-li
ne
inte
rsec
tion
s.F
or h
oriz
onta
l or
ver
tica
lse
gmen
ts,s
impl
y co
un
t sq
uar
es.F
or
diag
onal
seg
men
ts,u
se t
he
Pyt
hag
orea
nT
heo
rem
(pr
oven
in
Ch
apte
r 7)
.Th
is
theo
rem
sta
tes
that
in
an
y ri
ght
tria
ngl
e,if
th
e le
ngt
h o
f th
e lo
nge
st s
ide
(th
e si
deop
posi
te t
he
righ
t an
gle)
is
can
d th
e tw
osh
orte
r si
des
hav
e le
ngt
hs
aan
d b,
then
c2
�a2
�b2
.
Fin
d t
he
mea
sure
of
E �F�
on t
he
grid
at
the
righ
t.L
ocat
e a
righ
t tr
ian
gle
wit
h E �
F�as
its
lo
nge
st s
ide.
EF
��
22�
5�
2 ���
29��
5.4
un
its
Fin
d e
ach
mea
sure
to
the
nea
rest
ten
th o
f a
un
it.
1.I�J�
32.
M�N�
73.
R�S�
4.2
4.Q�
S�5.
8
5.I�K�
7.6
6.J�K�
57.
L�M�
4.1
8.L�
N�7.
2
Use
th
e gr
id a
bov
e.F
ind
th
e p
erim
eter
of
each
tri
angl
e to
th
e n
eare
st t
enth
of
a u
nit
.
9.�
AB
C20
.210
.�
QR
S18
11.
�D
EF
16.6
12.
�L
MN
18.3
An
swer
s sh
ow
n a
re f
ou
nd
by
rou
nd
ing
seg
men
t le
ng
ths
bef
ore
ad
din
g.
13.O
f al
l th
e se
gmen
ts s
how
n o
n t
he
14.O
n t
he
grid
,1 u
nit
�0.
5 cm
.How
can
th
e
grid
,wh
ich
is
lon
gest
? W
hat
is
its
answ
ers
abov
e be
use
d to
fin
d th
e m
easu
res
len
gth
?B
C�
8.1
in c
enti
met
ers?
D
ivid
e by
2 o
r m
ulti
ply
by
0.5.
15.U
se y
our
answ
er f
rom
exe
rcis
e 8
to16
.Use
a c
enti
met
er r
ule
r to
fin
d th
e pe
rim
eter
ca
lcu
late
th
e le
ngt
h o
f se
gmen
t L
Nof
tri
angl
e IJ
Kto
th
e n
eare
st t
enth
of
a
in c
enti
met
ers.
Ch
eck
by m
easu
rin
gce
nti
met
er.
7.8
cmw
ith
a c
enti
met
er r
ule
r.3.
6 cm
E 2
5F
A B F
I J
KN
M
C
D
E
S
R Q L
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
1-3
Exam
ple
Exam
ple
Answers (Lesson 1-3)
© Glencoe/McGraw-Hill A11 Glencoe Geometry
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
An
gle
Mea
sure
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-4
1-4
©G
lenc
oe/M
cGra
w-H
ill19
Gle
ncoe
Geo
met
ry
Lesson 1-4
Mea
sure
An
gle
sIf
tw
o n
onco
llin
ear
rays
hav
e a
com
mon
en
dpoi
nt,
they
for
m a
n a
ngl
e.T
he
rays
are
th
e si
des
of t
he
angl
e.T
he
com
mon
en
dpoi
nt
is t
he
vert
ex.T
he
angl
e at
th
e ri
ght
can
be
nam
ed a
s �
A,�
BA
C,�
CA
B,o
r �
1.
A r
igh
t an
gle
is a
n a
ngl
e w
hos
e m
easu
re i
s 90
.An
acu
te a
ngl
eh
as m
easu
re l
ess
than
90.
An
ob
tuse
an
gle
has
mea
sure
gre
ater
th
an 9
0 bu
t le
ss t
han
180
.
AC
B
1
a.N
ame
all
angl
es t
hat
hav
e R
as a
vert
ex.
Th
ree
angl
es a
re �
1,�
2,an
d �
3.F
orot
her
an
gles
,use
th
ree
lett
ers
to n
ame
them
:�S
RQ
,�P
RT
,an
d �
SR
T.
b.
Nam
e th
e si
des
of
�1.
RS
� �� ,
RP
���
SR
T
PQ
12
3
Mea
sure
eac
h a
ngl
e an
dcl
assi
fy i
t as
rig
ht,
acu
te,o
r ob
tuse
.
a.�
AB
DU
sin
g a
prot
ract
or,m
�A
BD
�50
.50
�90
,so
�A
BD
is a
n a
cute
an
gle.
b.
�D
BC
Usi
ng
a pr
otra
ctor
,m�
DB
C�
115.
180
�11
5 �
90,s
o �
DB
Cis
an
obt
use
angl
e.
c.�
EB
CU
sin
g a
prot
ract
or,m
�E
BC
�90
.�
EB
Cis
a r
igh
t an
gle.
BA
DE
C
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Ref
er t
o th
e fi
gure
.
1.N
ame
the
vert
ex o
f �
4.B
2.N
ame
the
side
s of
�B
DC
.D
B��
� ,D
C��
�
3.W
rite
an
oth
er n
ame
for
�D
BC
.�
3 o
r �
CB
D
Mea
sure
eac
h a
ngl
e in
th
e fi
gure
an
d c
lass
ify
it a
s ri
ght,
acu
te,o
r ob
tuse
.
4.�
MP
R12
0;o
btu
se
5.�
RP
N90
;ri
gh
t
6.�
NP
S45
;ac
ute
P
NM
R
S
C
BA
12
34
D
©G
lenc
oe/M
cGra
w-H
ill20
Gle
ncoe
Geo
met
ry
Co
ng
ruen
t A
ng
les
An
gles
th
at h
ave
the
sam
e m
easu
re a
re
con
gru
ent
angl
es.A
ray
th
at d
ivid
es a
n a
ngl
e in
to t
wo
con
gru
ent
angl
es i
s ca
lled
an
an
gle
bis
ecto
r.In
th
e fi
gure
,PN
� ��
is t
he
angl
e bi
sect
or o
f �
MP
R.P
oin
t N
lies
in
th
e in
teri
or o
f �
MP
Ran
d �
MP
N�
�N
PR
. Ref
er t
o th
e fi
gure
ab
ove.
If m
�M
PN
�2x
�14
an
d
m�
NP
R�
x�
34,f
ind
xan
d f
ind
m�
MP
R.
Sin
ce P
N� �
�bi
sect
s �
MP
R,�
MP
N�
�N
PR
,or
m�
MP
N�
m�
NP
R.
2x�
14 �
x�
34m
�N
PR
�(2
x�
14)
�(x
�34
)2x
�14
�x
�x
�34
�x
�54
�54
x�
14 �
34�
108
x�
14 �
14 �
34 �
14x
�20
QS
� ��
bis
ects
�P
QT
,an
d Q
P��
�an
d Q
R��
�ar
e op
pos
ite
rays
.
1.If
m�
PQ
T�
60 a
nd
m�
PQ
S�
4x�
14,f
ind
the
valu
e of
x.
4
2.If
m�
PQ
S�
3x�
13 a
nd
m�
SQ
T�
6x�
2,fi
nd
m�
PQ
T.
56
BA
���
and
BC
���
are
opp
osit
e ra
ys,B
F��
�b
isec
ts �
CB
E,a
nd
B
D� �
�b
isec
ts �
AB
E.
3.If
m�
EB
F�
6x�
4 an
d m
�C
BF
�7x
�2,
fin
d m
�E
BC
.
80
4.If
m�
1 �
4x�
10 a
nd
m�
2 �
5x,f
ind
m�
2.
50
5.If
m�
2 �
6y�
2 an
d m
�1
�8y
�14
,fin
d m
�A
BE
.
100
6.Is
�D
BF
a ri
ght
angl
e? E
xpla
in.
Yes;
sin
ce B
D��
�an
d B
F��
� are
bis
ecto
rs,m
�2
�m
�3
mu
st e
qu
al h
alf
the
tota
l an
gle
mea
sure
,an
d h
alf
of
180
is 9
0.
BA
CF
ED
12
34
QP
R
TS
PR
NM
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
An
gle
Mea
sure
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-4
1-4
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 1-4)
© Glencoe/McGraw-Hill A12 Glencoe Geometry
Skil
ls P
ract
ice
An
gle
Mea
sure
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-4
1-4
©G
lenc
oe/M
cGra
w-H
ill21
Gle
ncoe
Geo
met
ry
Lesson 1-4
For
Exe
rcis
es 1
–12,
use
th
e fi
gure
at
the
righ
t.
Nam
e th
e ve
rtex
of
each
an
gle.
1.�
4T
2.�
1W
3.�
2V
4.�
5T
Nam
e th
e si
des
of
each
an
gle.
5.�
46.
�5
TU��
� ,T
S���
TS��� ,
TW��
�
7.�
ST
V8.
�1
TS��� ,
TV��
�W
T��
� ,W
V��
�
Wri
te a
not
her
nam
e fo
r ea
ch a
ngl
e.
9.�
310
.�4
�W
TV
,�V
TW
�U
TS
,�S
TU
11.�
WT
S12
.�2
�S
TW
,�5
�W
VT
,�T
VW
,�W
VU
,�U
VW
Mea
sure
eac
h a
ngl
e an
d c
lass
ify
it a
s ri
ght,
acu
te,
or o
btu
se.
13.�
NM
P14
.�O
MN
90�,
rig
ht
40�,
acu
te
15.�
QM
N16
.�Q
MO
140�
,ob
tuse
100�
,ob
tuse
ALG
EBR
AIn
th
e fi
gure
,BA
���
and
BC
���
are
opp
osit
e ra
ys,
BD
� ��
bis
ects
�E
BC
,an
d B
F��
�b
isec
ts �
AB
E.
17.I
f m
�E
BD
�4x
�16
an
d m
�D
BC
�6x
�4,
fin
d m
�E
BD
.40
18.I
f m
�A
BF
�7x
�8
and
m�
EB
F�
5x�
10,
fin
d m
�E
BF
.55
BC
A
FE
D
MN
L
QO
P
U T VW
S5
3 21
4
©G
lenc
oe/M
cGra
w-H
ill22
Gle
ncoe
Geo
met
ry
For
Exe
rcis
es 1
–10,
use
th
e fi
gure
at
the
righ
t.
Nam
e th
e ve
rtex
of
each
an
gle.
1.�
5M
2.�
3P
3.�
8O
4.�
NM
PM
Nam
e th
e si
des
of
each
an
gle.
5.�
66.
�2
NM
��� ,
NO
���
or
NP
���
or
NR
���
PR��
� ,P
M��
�
7.�
MO
P8.
�O
MN
OM
��� ,
OP
��� o
r O
R��
�M
O��
� ,M
N��
�
Wri
te a
not
her
nam
e fo
r ea
ch a
ngl
e.
9.�
QP
R10
.�1
�3,
�R
PQ
�M
PO
,�O
PM
,�M
PN
,�N
PM
Mea
sure
eac
h a
ngl
e an
d c
lass
ify
it a
s ri
ght,
acu
te,
or o
btu
se.
11.�
UZ
W12
.�Y
ZW
90�,
rig
ht
70�,
acu
te
13.�
TZ
W14
.�U
ZT
110�
,ob
tuse
20�,
acu
te
ALG
EBR
AIn
th
e fi
gure
,CB
���
and
CD
���
are
opp
osit
e ra
ys,
CE
� ��
bis
ects
�D
CF
,an
d C
G��
�b
isec
ts �
FC
B.
15.I
f m
�D
CE
�4x
�15
an
d m
�E
CF
�6x
�5,
fin
d m
�D
CE
.55
16.I
f m
�F
CG
�9x
�3
and
m�
GC
B�
13x
�9,
fin
d m
�G
CB
.30
17.T
RA
FFIC
SIG
NS
Th
e di
agra
m s
how
s a
sign
use
d to
war
n
driv
ers
of a
sch
ool
zon
e or
cro
ssin
g.M
easu
re a
nd
clas
sify
ea
ch n
um
bere
d an
gle.
m�
1 �
90,r
igh
t an
gle
;m
�2
�13
0,o
btu
se
2 1BC
G
F
EDZ
YT
U
VW
X
N
O
PQ
R
M1 2
8
3
54
6
7
Pra
ctic
e (
Ave
rag
e)
An
gle
Mea
sure
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-4
1-4
Answers (Lesson 1-4)
© Glencoe/McGraw-Hill A13 Glencoe Geometry
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csA
ng
le M
easu
re
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-4
1-4
©G
lenc
oe/M
cGra
w-H
ill23
Gle
ncoe
Geo
met
ry
Lesson 1-4
Pre-
Act
ivit
yH
ow b
ig i
s a
deg
ree?
Rea
d th
e in
trod
uct
ion
to
Les
son
1-4
at
the
top
of p
age
29 i
n y
our
text
book
.•
A s
emic
ircl
e is
hal
f a
circ
le.H
ow m
any
degr
ees
are
ther
e in
a
sem
icir
cle?
180
•H
ow m
any
degr
ees
are
ther
e in
a q
uar
ter
circ
le?
90
Rea
din
g t
he
Less
on
1.M
atch
eac
h d
escr
ipti
on i
n t
he
firs
t co
lum
n w
ith
on
e of
th
e te
rms
in t
he
seco
nd
colu
mn
.S
ome
term
s in
th
e se
con
d co
lum
n m
ay b
e u
sed
mor
e th
an o
nce
or
not
at
all.
a.a
figu
re m
ade
up
of t
wo
non
coll
inea
r ra
ys w
ith
a1.
vert
ex
com
mon
en
dpoi
nt
42.
angl
e bi
sect
orb
.an
gles
wh
ose
degr
ee m
easu
res
are
less
th
an 9
08
3.op
posi
te r
ays
c.an
gles
th
at h
ave
the
sam
e m
easu
re6
4.an
gle
d.
angl
es w
hos
e de
gree
mea
sure
s ar
e be
twee
n 9
0 an
d 18
05
5.ob
tuse
an
gles
e.a
tool
use
d to
mea
sure
an
gles
106.
con
gru
ent
angl
esf.
the
com
mon
en
dpoi
nt
of t
he
rays
th
at f
orm
an
an
gle
17.
righ
t an
gles
g.a
ray
that
div
ides
an
an
gle
into
tw
o co
ngr
uen
t an
gles
28.
acu
te a
ngl
es9.
com
pass
10.p
rotr
acto
r2.
Use
th
e fi
gure
to
nam
e ea
ch o
f th
e fo
llow
ing.
a.a
righ
t an
gle
�A
BE
or
�E
BG
b.
an o
btu
se a
ngl
e�
AB
Fo
r �
AB
Cc.
an a
cute
an
gle
�E
BF
,�F
BC
,�C
BG
,�E
BC
,or
�F
BG
d.
a po
int
in t
he
inte
rior
of
�E
BC
Fe.
a po
int
in t
he
exte
rior
of
�E
BA
F,C
,or
Gf.
the
angl
e bi
sect
or o
f �
EB
CB
F��
�
g.a
poin
t on
�C
BE
C,B
,or
Eh
.th
e si
des
of �
AB
FB
A��
�an
d B
F��
�
i.a
pair
of
oppo
site
ray
sB
A��
�an
d B
G��
�
j.th
e co
mm
on v
erte
x of
all
an
gles
sh
own
in
th
e fi
gure
Bk
.a
pair
of
con
gru
ent
angl
es�
EB
Fan
d �
FB
C,o
r �
AB
Ean
d �
EB
Gl.
the
angl
e w
ith
th
e gr
eate
st m
easu
re�
AB
G
Hel
pin
g Y
ou
Rem
emb
er3.
A g
ood
way
to
rem
embe
r re
late
d ge
omet
ric
idea
s is
to
com
pare
th
em a
nd
see
how
th
eyar
e al
ike
and
how
th
ey a
re d
iffe
ren
t.G
ive
som
e si
mil
arit
ies
and
diff
eren
ces
betw
een
con
gru
ent
segm
ents
and
con
gru
ent
angl
es.
Sam
ple
an
swer
:C
on
gru
ent
seg
men
ts a
nd
co
ng
ruen
t an
gle
s ar
e al
ike
bec
ause
th
ey b
oth
invo
lve
a p
air
of
fig
ure
s w
ith
th
e sa
me
mea
sure
.Th
eyar
e d
iffe
ren
t b
ecau
se c
on
gru
ent
seg
men
ts h
ave
the
sam
e le
ng
th,w
hic
hca
n b
e m
easu
red
in u
nit
s su
ch a
s in
ches
or
cen
tim
eter
s,w
hile
co
ng
ruen
tan
gle
s h
ave
the
sam
e d
egre
e m
easu
re.
BG
28� 28
�
A
EF
CD
©G
lenc
oe/M
cGra
w-H
ill24
Gle
ncoe
Geo
met
ry
An
gle
Rel
atio
nsh
ips
An
gles
are
mea
sure
d in
deg
rees
(�)
.Eac
h d
egre
e of
an
an
gle
is d
ivid
-ed
in
to 6
0 m
inu
tes
(�),
and
each
min
ute
of
an a
ngl
e is
di
vide
d in
to 6
0 se
con
ds (
).
60�
�1�
60
�1�
67�1 2� �
�67
�30�
70.4
��
70°2
4�
90�
�89
°60�
Tw
o an
gles
are
com
ple
men
tary
if
the
sum
of
thei
r m
easu
res
is 9
0�.
Fin
d t
he
com
ple
men
t of
eac
h o
f th
e fo
llow
ing
angl
es.
1.35
�15�
2.27
�16�
3.15
�54�
54�4
5�62
�44�
74�0
6�
4.29
�18�
22
5.34
�29�
45
6.87
�2�3
60�4
1�38
�55
�30�
15�
2�57
�57
�
Tw
o an
gles
are
su
pp
lem
enta
ry i
f th
e su
m o
f th
eir
mea
sure
s is
180
�.F
ind
th
e su
pp
lem
ent
of e
ach
of
the
foll
owin
g an
gles
.
7.12
0�18
�8.
84�1
2�9.
110�
2�
59�4
2�95
�48�
69�5
8�
10.4
5�16
�24
11.3
9�21
�54
12.1
29�1
8�36
134�
43�3
6�14
0�38
�6�
50�4
1�24
�
13.9
8�52
�59
14.9
�2�3
215
.1�2
�3
81�7
�1�
170�
57�2
8�17
8�57
�57
�
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-4
1-4
Answers (Lesson 1-4)
© Glencoe/McGraw-Hill A14 Glencoe Geometry
Stu
dy G
uid
e a
nd I
nte
rven
tion
An
gle
Rel
atio
nsh
ips
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-5
1-5
©G
lenc
oe/M
cGra
w-H
ill25
Gle
ncoe
Geo
met
ry
Lesson 1-5
Pair
s o
f A
ng
les
Ad
jace
nt
angl
esar
e an
gles
in
th
e sa
me
plan
e th
at h
ave
a co
mm
onve
rtex
an
d a
com
mon
sid
e,bu
t n
o co
mm
on i
nte
rior
poi
nts
.Ver
tica
l an
gles
are
two
non
adja
cen
t an
gles
for
med
by
two
inte
rsec
tin
g li
nes
.A p
air
of a
djac
ent
angl
es w
hos
en
onco
mm
on s
ides
are
opp
osit
e ra
ys i
s ca
lled
a l
inea
r p
air.
Iden
tify
eac
h p
air
of a
ngl
es a
s a
dja
cen
t a
ngl
es,v
erti
cal
an
gles
,an
d/o
r as
a l
inea
r p
air
.
Exam
ple
Exam
ple
a.
�S
RT
and
�T
RU
hav
e a
com
mon
vert
ex a
nd
a co
mm
on s
ide,
but
no
com
mon
in
teri
or p
oin
ts.T
hey
are
adja
cen
t an
gles
.
c.
�6
and
�5
are
adja
cen
t an
gles
wh
ose
non
com
mon
sid
es a
re o
ppos
ite
rays
.T
he
angl
es f
orm
a l
inea
r pa
ir.
D
CB
A
56
RUT
Sb
.
�1
and
�3
are
non
adja
cen
t an
gles
for
med
by t
wo
inte
rsec
tin
g li
nes
.Th
ey a
re v
erti
cal
angl
es.�
2 an
d �
4 ar
e al
so v
erti
cal
angl
es.
d.
�A
and
�B
are
two
angl
es w
hos
e m
easu
res
hav
e a
sum
of
90.T
hey
are
com
plem
enta
ry.
�F
and
�G
are
two
angl
es w
hos
e m
easu
res
hav
e a
sum
of
180.
Th
ey a
re s
upp
lem
enta
ry.
AB
FG
30�
60�
60�
120�
N
RP
SM
14
32
Exer
cises
Exer
cises
Iden
tify
eac
h p
air
of a
ngl
es a
s a
dja
cen
t,ve
rtic
al,
and
/or
as a
lin
ear
pa
ir.
1.�
1 an
d �
22.
�1
and
�6
adja
cen
tlin
ear
pai
r;ad
jace
nt
3.�
1 an
d �
54.
�3
and
�2
vert
ical
adja
cen
t
For
Exe
rcis
es 5
–7,r
efer
to
the
figu
re a
t th
e ri
ght.
5.Id
enti
fy t
wo
obtu
se v
erti
cal
angl
es.
�R
NT
and
�S
NU
6.Id
enti
fy t
wo
acu
te a
djac
ent
angl
es.
�R
NV
an
d�
VN
To
r �
VN
Tan
d �
TN
U7.
Iden
tify
an
an
gle
supp
lem
enta
ry t
o �
TN
U.
�U
NS
or
�T
NR
8.F
ind
the
mea
sure
s of
tw
o co
mpl
emen
tary
ang
les
if t
he d
iffe
renc
e in
the
ir m
easu
res
is 1
8.36
an
d 5
4
RS
NU
TV
RS
TU
V
P
Q5
43
21
6
©G
lenc
oe/M
cGra
w-H
ill26
Gle
ncoe
Geo
met
ry
Perp
end
icu
lar
Lin
esL
ines
,ray
s,an
d se
gmen
ts t
hat
for
m f
our
righ
t an
gles
are
per
pen
dic
ula
r.T
he
righ
t an
gle
sym
bol
indi
cate
s th
at t
he
lin
es
are
perp
endi
cula
r.In
th
e fi
gure
at
the
righ
t,A
C� �
�is
per
pen
dicu
lar
to B
D��
� ,or
AC
� ��
⊥B
D��
� .
Fin
d x
so t
hat
D �Z�
⊥P�
Z�.
If D �
Z�⊥
P�Z�
,th
en m
�D
ZP
�90
.
m�
DZ
Q�
m�
QZ
P�
m�
DZ
PS
um o
f pa
rts
�w
hole
(9x
�5)
�(3
x�
1)�
90S
ubst
itutio
n
12x
�6
�90
Sim
plify
.12
x�
84S
ubtr
act
6 fr
om e
ach
side
.
x�
7D
ivid
e ea
ch s
ide
by 1
2.
1.F
ind
xan
d y
so t
hat
NR
���
⊥M
Q��
� .x
�15
,y�
8
2.F
ind
m�
MS
N.9
0
3.m
�E
BF
�3x
�10
,m�
DB
E�
x,an
d B
D��
�⊥
BF
��� .
Fin
d x.
x�
20
4.If
m�
EB
F�
7y�
3 an
d m
�F
BC
�3y
�3,
fin
d y
so
that
EB
� �� ⊥
BC
��� .
9
5.F
ind
x,m
�P
QS
,an
d m
�S
QR
.
x�
8,m
�P
QS
�24
,m�
SQ
R�
66
6.F
ind
y,m
�R
PT,
and
m�
TP
W.
y�
15,m
�R
PT
�55
,m�
TP
W�
35
P
S
V
R
W
T(4
y �
5)�
(2y
� 5
)�QR
PS
3x� (8
x �
2)�
BC
A
DE
F
M
N RSQP
x�5x
�
(9y
� 1
8)�
Z
D
P
Q(9
x �
5)� (3
x �
1)�
B CDA
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
An
gle
Rel
atio
nsh
ips
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-5
1-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 1-5)
© Glencoe/McGraw-Hill A15 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
An
gle
Rel
atio
nsh
ips
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-5
1-5
©G
lenc
oe/M
cGra
w-H
ill27
Gle
ncoe
Geo
met
ry
Lesson 1-5
For
Exe
rcis
es 1
–6,u
se t
he
figu
re a
t th
e ri
ght
and
a
pro
trac
tor.
1.N
ame
two
acu
te v
erti
cal
angl
es.
�E
KH
,�F
KG
2.N
ame
two
obtu
se v
erti
cal
angl
es.
�E
KF
,�H
KG
3.N
ame
a li
nea
r pa
ir.
Sam
ple
an
swer
:�
EK
H,�
EK
F
4.N
ame
two
acu
te a
djac
ent
angl
es.
�F
KG
,�G
KJ
5.N
ame
an a
ngl
e co
mpl
emen
tary
to
�E
KH
.�
GK
J
6.N
ame
an a
ngl
e su
pple
men
tary
to
�F
KG
.�
EK
Fo
r �
GK
H
7.F
ind
the
mea
sure
s of
an
an
gle
and
its
com
plem
ent
if o
ne
angl
e m
easu
res
18 d
egre
esm
ore
than
th
e ot
her
.36
,54
8.T
he
mea
sure
of
the
supp
lem
ent
of a
n a
ngl
e is
36
less
th
an t
he
mea
sure
of
the
angl
e.F
ind
the
mea
sure
s of
th
e an
gles
.72
,108
ALG
EBR
AF
or E
xerc
ises
9–1
0,u
se t
he
figu
re a
t th
e ri
ght.
9.If
m�
RT
S�
8x�
18,f
ind
xso
th
at T
R��
�⊥
TS
��� .
9
10.I
f m
�P
TQ
�3y
�10
an
d m
�Q
TR
�y,
fin
d y
so t
hat
�
PT
Ris
a r
igh
t an
gle.
25
Det
erm
ine
wh
eth
er e
ach
sta
tem
ent
can
be
assu
med
fr
om t
he
figu
re.E
xpla
in.
11.�
WZ
Uis
a r
igh
t an
gle.
Yes;
it is
mar
ked
wit
h a
rig
ht
ang
le s
ymb
ol.
12.�
YZ
Uan
d �
UZ
V a
re s
upp
lem
enta
ry.
Yes;
the
sum
of
thei
r m
easu
res
is 1
80 s
ince
th
e an
gle
s fo
rm a
lin
ear
pai
r.
13.�
VZ
Uis
adj
acen
t to
�Y
ZX
.
No
;th
e an
gle
s d
o n
ot
shar
e a
com
mo
n s
ide.
ZX
W
V
Y
U
TP
QR
S
K
G
J
FE H
©G
lenc
oe/M
cGra
w-H
ill28
Gle
ncoe
Geo
met
ry
For
Exe
rcis
es 1
–4,u
se t
he
figu
re a
t th
e ri
ght
and
a
pro
trac
tor.
1.N
ame
two
obtu
se v
erti
cal
angl
es.
Sam
ple
an
swer
:�
GF
H,�
CF
E2.
Nam
e a
lin
ear
pair
wh
ose
vert
ex i
s B
.�
GB
C,�
CB
A
3.N
ame
an a
ngl
e n
ot a
djac
ent
to b
ut
com
plem
enta
ry t
o �
FG
C.
�F
ED
4.N
ame
an a
ngl
e ad
jace
nt
and
supp
lem
enta
ry t
o �
DC
B.
�B
CG
or
�D
CH
5.T
wo
angl
es a
re c
ompl
emen
tary
.Th
e m
easu
re o
f on
e an
gle
is 2
1 m
ore
than
tw
ice
the
mea
sure
of
the
oth
er a
ngl
e.F
ind
the
mea
sure
s of
th
e an
gles
.23
,67
6.If
a s
upp
lem
ent
of a
n a
ngl
e h
as a
mea
sure
78
less
th
an t
he
mea
sure
of
the
angl
e,w
hat
are
the
mea
sure
s of
th
e an
gles
?12
9,51
AL
GE
BR
AF
or E
xerc
ises
7–8
,use
th
e fi
gure
at
the
righ
t.
7.If
m�
FG
E�
5x�
10,f
ind
xso
th
at
FC
� ��
⊥A
E��
� .16
8.If
m�
BG
C�
16x
�4
and
m�
CG
D�
2x�
13,
fin
d x
so t
hat
�B
GD
is a
rig
ht
angl
e.4.
5
Det
erm
ine
wh
eth
er e
ach
sta
tem
ent
can
be
assu
med
fro
m t
he
figu
re.E
xpla
in.
9.�
NQ
Oan
d �
OQ
Par
e co
mpl
emen
tary
.
No
;m
�N
QP
is n
ot
kno
wn
to
be
90.
10.�
SR
Qan
d �
QR
Pis
a l
inea
r pa
ir.
Yes;
they
are
ad
jace
nt
ang
les
wh
ose
no
nco
mm
on
sid
es a
re o
pp
osi
te r
ays.
11.�
MQ
Nan
d �
MQ
Rar
e ve
rtic
al a
ngl
es.
No
;th
e an
gle
s ar
e ad
jace
nt.
12.S
TREE
T M
APS
Dar
ren
ske
tch
ed a
map
of
the
cros
s st
reet
s n
eare
st
to h
is h
ome
for
his
fri
end
Mig
uel
.Des
crib
e tw
o di
ffer
ent
angl
ere
lati
onsh
ips
betw
een
th
e st
reet
s.
Sam
ple
an
swer
:B
eaco
n ⊥
Mai
n;
Oliv
e d
ivid
es t
wo
of
the
ang
les
form
ed b
y B
aco
n a
nd
Mai
n in
to p
airs
of
com
ple
men
tary
an
gle
s.
Oliv
e
Beacon
Main
Q
O
P
RS
M
N
GF
AB
E
D
C
DA
E
HG
BC
F
Pra
ctic
e (
Ave
rag
e)
An
gle
Rel
atio
nsh
ips
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-5
1-5
Answers (Lesson 1-5)
© Glencoe/McGraw-Hill A16 Glencoe Geometry
Readin
g t
o L
earn
Math
em
ati
csA
ng
le R
elat
ion
ship
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-5
1-5
©G
lenc
oe/M
cGra
w-H
ill29
Gle
ncoe
Geo
met
ry
Lesson 1-5
Pre-
Act
ivit
yW
hat
kin
ds
of a
ngl
es a
re f
orm
ed w
hen
str
eets
in
ters
ect?
Rea
d th
e in
trod
uct
ion
to
Les
son
1-5
at
the
top
of p
age
37 i
n y
our
text
book
.
•H
ow m
any
sepa
rate
ang
les
are
form
ed if
thr
ee li
nes
inte
rsec
t at
a c
omm
onpo
int?
(Do
not
use
an a
ngle
who
se in
teri
or in
clud
es p
art
of a
noth
er a
ngle
.)6
•H
ow m
any
sepa
rate
ang
les
are
form
ed if
nlin
es in
ters
ect
at a
com
mon
poin
t? (D
o no
t co
unt
an a
ngle
who
se in
teri
or in
clud
es p
art
of a
noth
er a
ngle
.)2n
Rea
din
g t
he
Less
on
1.N
ame
each
of
the
foll
owin
g in
th
e fi
gure
at
the
righ
t.
a.tw
o pa
irs
of c
ongr
uen
t an
gles
�1
and
�3,
�2
and
�4
b.
a pa
ir o
f ac
ute
ver
tica
l an
gles
�2
and
�4
c.a
pair
of
obtu
se v
erti
cal
angl
es�
1 an
d �
3d
.fo
ur
pair
s of
adj
acen
t an
gles
�1
and
�2,
�2
and
�3,
�3
and
�4,
�4
and
�1
e.tw
o pa
irs
of v
erti
cal
angl
es�
1 an
d �
3,�
2 an
d �
4f.
fou
r li
nea
r pa
irs
�1
and
�2,
�2
and
�3,
�3
and
�4,
�4
and
�1
g.fo
ur
pair
s of
su
pple
men
tary
an
gles
�1
and
�2,
�2
and
�3,
�3
and
�4,
�4
and
�1
2.T
ell
wh
eth
er e
ach
sta
tem
ent
is a
lway
s,so
met
imes
,or
nev
ertr
ue.
a.If
tw
o an
gles
are
adj
acen
t an
gles
,th
ey f
orm
a l
inea
r pa
ir.
som
etim
esb
.If
tw
o an
gles
for
m a
lin
ear
pair
,th
ey a
re c
ompl
emen
tary
.n
ever
c.If
tw
o an
gles
are
su
pple
men
tary
,th
ey a
re c
ongr
uen
t.so
met
imes
d.
If t
wo
angl
es a
re c
ompl
emen
tary
,th
ey a
re a
djac
ent.
som
etim
ese.
Wh
en t
wo
perp
endi
cula
r li
nes
in
ters
ect,
fou
r co
ngr
uen
t an
gles
are
for
med
.al
way
sf.
Ver
tica
l an
gles
are
su
pple
men
tary
.so
met
imes
g.V
erti
cal
angl
es a
re c
ompl
emen
tary
.so
met
imes
h.
Th
e tw
o an
gles
in
a l
inea
r pa
ir a
re b
oth
acu
te.
nev
eri.
If t
wo
angl
es f
orm
a l
inea
r pa
ir,o
ne
is a
cute
an
d th
e ot
her
is
obtu
se.
som
etim
es
3.C
ompl
ete
each
sen
ten
ce.
a.If
tw
o an
gles
are
su
pple
men
tary
an
d x
is t
he
mea
sure
of
one
of t
he
angl
es,t
hen
th
em
easu
re o
f th
e ot
her
an
gle
is
.
b.
If t
wo
angl
es a
re c
ompl
emen
tary
an
d x
is t
he
mea
sure
of
one
of t
he
angl
es,t
hen
th
em
easu
re o
f th
e ot
her
an
gle
is
.
Hel
pin
g Y
ou
Rem
emb
er4.
Loo
k u
p th
e n
onm
ath
emat
ical
mea
nin
g of
su
pple
men
tary
in y
our
dict
ion
ary.
How
can
this
def
init
ion
hel
p yo
u t
o re
mem
ber
the
mea
nin
g of
su
pple
men
tary
an
gles
?S
amp
lean
swer
:S
up
ple
men
tary
mea
ns
som
eth
ing
ad
ded
to
co
mp
lete
a t
hin
g.
An
an
gle
an
d it
s su
pp
lem
ent
can
be
join
ed t
o o
bta
in a
lin
ear
pai
r.
90 �
x
180
�x
65�
23
41
©G
lenc
oe/M
cGra
w-H
ill30
Gle
ncoe
Geo
met
ry
Cu
rve
Sti
tch
ing
Th
e st
ar d
esig
n a
t th
e ri
ght
was
cre
ated
by
a m
eth
od k
now
n a
s cu
rve
stit
chin
g.A
lth
ough
th
e de
sign
app
ears
to
con
tain
cu
rves
,it
is m
ade
up
enti
rely
of
lin
e se
gmen
ts.
To
begi
n t
he
star
des
ign
,dra
w a
60°
angl
e.M
ark
eigh
t eq
ual
ly-s
pace
d po
ints
on
eac
h r
ay,a
nd
nu
mbe
r th
e po
ints
as
show
n b
elow
.Th
en c
onn
ect
pair
s of
poi
nts
th
at h
ave
the
sam
e n
um
ber.
To
mak
e a
com
plet
e st
ar,m
ake
the
sam
e de
sign
in
si
x 60
°an
gles
th
at h
ave
a co
mm
on c
entr
al v
erte
x.
1.C
ompl
ete
the
sect
ion
of
the
star
des
ign
abo
ve b
y co
nn
ecti
ng
pair
s of
poi
nts
th
at h
ave
the
sam
e n
um
ber.
2.C
ompl
ete
the
foll
owin
g de
sign
.
3.C
reat
e yo
ur
own
des
ign
.You
may
use
sev
eral
an
gles
,an
d th
e an
gles
may
ove
rlap
.S
ee s
tud
ents
’wo
rk.
12
34
56
78
9
11
11
12
13
14
15
16
17
18
19
1
2
3
4
5
6
7
8
9
1213
1415
1617
1819
8
7
6
5
4
3
2
1
12
34
56
78
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-5
1-5
Answers (Lesson 1-5)
© Glencoe/McGraw-Hill A17 Glencoe Geometry
An
swer
s
Answers (Lesson 1-6)
Stu
dy G
uid
e a
nd I
nte
rven
tion
Po
lyg
on
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-6
1-6
©G
lenc
oe/M
cGra
w-H
ill31
Gle
ncoe
Geo
met
ry
Lesson 1-6
Poly
go
ns
A p
olyg
onis
a c
lose
d fi
gure
for
med
by
a fi
nit
e n
um
ber
of c
opla
nar
lin
ese
gmen
ts.T
he
side
s th
at h
ave
a co
mm
on e
ndp
oin
t m
ust
be
non
coll
inea
r an
d ea
ch s
ide
inte
rsec
ts e
xact
ly t
wo
oth
er s
ides
at
thei
r en
dpoi
nts
.A p
olyg
on i
s n
amed
acc
ordi
ng
to i
tsn
um
ber
of s
ides
.A r
egu
lar
pol
ygon
has
con
gru
ent
side
s an
d co
ngr
uen
t an
gles
.A p
olyg
onca
n b
e co
nca
veor
con
vex.
Nam
e ea
ch p
olyg
on b
y it
s n
um
ber
of
sid
es.T
hen
cla
ssif
y it
as
con
cave
or c
onve
xan
d r
egu
lar
or i
rreg
ula
r.
Exam
ple
Exam
ple
a.
Th
e po
lygo
n h
as 4
sid
es,s
o it
is
a qu
adri
late
ral.
It i
s co
nca
ve b
ecau
se p
art
of D �
E�or
E�F�
lies
in
th
ein
teri
or o
f th
e fi
gure
.Bec
ause
it
is c
onca
ve,i
tca
nn
ot h
ave
all
its
angl
es c
ongr
uen
t an
d so
it
isir
regu
lar.
c.
Th
e po
lygo
n h
as 5
sid
es,s
o it
is
a pe
nta
gon
.It
isco
nve
x.A
ll s
ides
are
con
gru
ent
and
all
angl
es a
reco
ngr
uen
t,so
it
is a
reg
ula
r pe
nta
gon
.
DF
GEb
.
Th
e fi
gure
is
not
clo
sed,
so i
t is
not
a p
olyg
on.
d.
Th
e fi
gure
has
8 c
ongr
uen
t si
des
and
8 co
ngr
uen
t an
gles
.It
isco
nve
x an
d is
a r
egu
lar
octa
gon
.
H
JK
LI
Exer
cises
Exer
cises
Nam
e ea
ch p
olyg
on b
y it
s n
um
ber
of
sid
es.T
hen
cla
ssif
y it
as
con
cave
or c
onve
xan
d r
egu
lar
or i
rreg
ula
r.
1.2.
3.
hex
ago
n;
conv
ex;
qu
adri
late
ral;
conv
ex;
pen
tag
on
;co
nca
ve;
reg
ula
rir
reg
ula
rir
reg
ula
r
4.5.
6.
tria
ng
le;
conv
ex;
pen
tag
on
;co
nca
ve;
oct
ago
n;
con
cave
;ir
reg
ula
rir
reg
ula
rir
reg
ula
r
©G
lenc
oe/M
cGra
w-H
ill32
Gle
ncoe
Geo
met
ry
Peri
met
erT
he
per
imet
erof
a p
olyg
on i
s th
e su
m o
f th
e le
ngt
hs
of a
ll t
he
side
s of
th
epo
lygo
n.T
her
e ar
e sp
ecia
l fo
rmu
las
for
the
peri
met
er o
f a
squ
are
or a
rec
tan
gle.
Wri
te a
n e
xpre
ssio
n o
r fo
rmu
la f
or t
he
per
imet
er o
f ea
ch p
olyg
on.
Fin
d t
he
per
imet
er.
Stu
dy G
uid
e a
nd I
nte
rven
tion
(con
tinued
)
Po
lyg
on
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-6
1-6
Exam
ple
Exam
ple
a.
P�
a�
b�
c�
3 �
4 �
5�
12 i
n.
b.
P�
4s�
4(5)
�20
cm
c.
P�
2 ��
2w�
2(3)
�2(
2)�
10 f
t
3 ft
2 ft
� �
ww
5 cm
5 cm
5 cm
5 cms s
ss
3 in
.5
in.
4 in
.
a
b c
Exer
cises
Exer
cises
Fin
d t
he
per
imet
er o
f ea
ch f
igu
re.
1.2.
9 cm
22 f
t
3.4.
96 y
d10
cm
Fin
d t
he
len
gth
of
each
sid
e of
th
e p
olyg
on f
or t
he
give
n p
erim
eter
.
5.P
�96
6.P
�48
16,3
28,
10,1
0,20
x
x
2x
x �
2
rect
angl
e
2 x
x
1 cm
24 y
d
19 y
d
12 y
d14
yd
27 y
d
squa
re
5.5
ft
3.5
cm
3 cm
2.5
cm
© Glencoe/McGraw-Hill A18 Glencoe Geometry
Skil
ls P
ract
ice
Po
lyg
on
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-6
1-6
©G
lenc
oe/M
cGra
w-H
ill33
Gle
ncoe
Geo
met
ry
Lesson 1-6
Nam
e ea
ch p
olyg
on b
y it
s n
um
ber
of
sid
es a
nd
th
en c
lass
ify
it a
s co
nve
xor
con
cave
and
reg
ula
ror
irr
egu
lar.
1.2.
3.
qu
adri
late
ral;
conv
ex;
tria
ng
le;
conv
ex;
pen
tag
on
;co
nca
ve;
irre
gu
lar
reg
ula
rir
reg
ula
r
4.5.
6.
hep
tag
on
;co
nvex
;q
uad
rila
tera
l;co
nvex
;d
od
ecag
on
;re
gu
lar
irre
gu
lar
con
cave
;ir
reg
ula
r
Fin
d t
he
per
imet
er o
f ea
ch f
igu
re.
7.8.
9.
98 y
d20
m32
in.
CO
OR
DIN
ATE
GEO
MET
RYF
ind
th
e p
erim
eter
of
each
pol
ygon
.
10.t
rian
gle
AB
Cw
ith
ver
tice
s A
(3,5
),B
(3,1
),an
d C
(0,1
)
12 u
nit
s
11.q
uad
rila
tera
l Q
RS
Tw
ith
ver
tice
s Q
(�3,
2),R
(1,2
),S
(1,�
4),a
nd
T(�
3,�
4)
20 u
nit
s
12.q
uad
rila
tera
l L
MN
Ow
ith
ver
tice
s L
(�1,
4),M
(3,4
),N
(2,1
),an
d O
(�2,
1)
�14
.3 u
nit
s
ALG
EBR
AF
ind
th
e le
ngt
h o
f ea
ch s
ide
of t
he
pol
ygon
for
th
e gi
ven
per
imet
er.
13.P
�10
4 m
illi
met
ers
14.P
�84
kil
omet
ers
15.P
�88
fee
t
All
are
13 m
m.
All
are
28 k
m.
9 ft
,9 f
t,35
ft,
35 f
t
4w �
1
w
10 in
.
10 in
.2
in.
2 in
.
2 in
.2
in.
2 in
.2
in.
5 m
2 m
3 m
6 m
4 m
40 y
d
20 y
d
18 y
d20
yd
©G
lenc
oe/M
cGra
w-H
ill34
Gle
ncoe
Geo
met
ry
Nam
e ea
ch p
olyg
on b
y it
s n
um
ber
of
sid
es a
nd
th
en c
lass
ify
it a
s co
nve
xor
con
cave
and
reg
ula
ror
irr
egu
lar.
1.2.
3.
hex
ago
n;
con
cave
;n
on
ago
n;
conv
ex;
qu
adri
late
ral;
irre
gu
lar
reg
ula
rco
nvex
;ir
reg
ula
r
Fin
d t
he
per
imet
er o
f ea
ch f
igu
re.
4.5.
6.
53 m
m86
mi
56 c
m
CO
OR
DIN
ATE
GEO
MET
RYF
ind
th
e p
erim
eter
of
each
pol
ygon
.
7.qu
adri
late
ral
OP
QR
wit
h v
erti
ces
O(�
3,2)
,P(1
,5),
Q(6
,4),
and
R(5
,�2)
�25
.1 u
nit
s
8.pe
nta
gon
ST
UV
Ww
ith
ver
tice
s S
(0,0
),T
(3,�
2),U
(2,�
5),V
(�2,
�5)
,an
d W
(�3,
�2)
�17
.5 u
nit
s
ALG
EBR
AF
ind
th
e le
ngt
h o
f ea
ch s
ide
of t
he
pol
ygon
for
th
e gi
ven
per
imet
er.
9.P
�26
in
ches
10.P
�39
cen
tim
eter
s11
.P�
89 f
eet
3 in
.,3
in.,
10 in
.,10
in.
17 c
m,1
7 cm
,5 c
m18
ft,
18 f
t,36
ft,
17 f
t
SEW
ING
For
Exe
rcis
es 1
2–13
,use
th
e fo
llow
ing
info
rmat
ion
.Ja
smin
e pl
ans
to s
ew f
rin
ge a
rou
nd
the
scar
f sh
own
in
th
e di
agra
m.
12.H
ow m
any
inch
es o
f fr
inge
doe
s sh
e n
eed
to p
urc
has
e?
40 in
.
13.I
f Ja
smin
e do
ubl
es t
he
wid
th o
f th
e sc
arf,
how
man
y in
ches
of
frin
ge w
ill
she
nee
d?
48 in
.
16 in
.
4 in
.4
in.
16 in
.
2x �
2
x �
9
5x �
4
3x �
5
2x �
3
6n �
8
n
14 c
m
14 c
m
4 cm
4 cm
6 cm
6 cm
6 cm
2 cm
32 m
i33 m
i21
mi
7 m
m
10 m
m18
mm
18 m
m
Pra
ctic
e (
Ave
rag
e)
Po
lyg
on
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-6
1-6
Answers (Lesson 1-6)
© Glencoe/McGraw-Hill A19 Glencoe Geometry
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csP
oly
go
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-6
1-6
©G
lenc
oe/M
cGra
w-H
ill35
Gle
ncoe
Geo
met
ry
Lesson 1-6
Pre-
Act
ivit
yH
ow a
re p
olyg
ons
rela
ted
to
toys
?
Rea
d th
e in
trod
uct
ion
to
Les
son
1-6
at
the
top
of p
age
45 i
n y
our
text
book
.
Nam
e fo
ur d
iffe
rent
sha
pes
that
can
eac
h be
form
ed b
y fo
ur s
tick
s co
nnec
ted
tofo
rm a
clo
sed
figu
re.A
ssu
me
you
hav
e st
icks
wit
h a
goo
d va
riet
y of
len
gth
s.S
amp
le a
nsw
er:
squ
are,
rect
ang
le,p
aral
lelo
gra
m,t
rap
ezo
id
Rea
din
g t
he
Less
on
1.T
ell
wh
y ea
ch f
igu
re i
s n
ota
poly
gon
.
a.b
.c.
no
t cl
ose
dcu
rved
(n
ot
all m
ade
Sid
es in
ters
ect
at a
po
int
up
of
seg
men
ts)
that
is n
ot
an e
nd
po
int.
2.N
ame
each
pol
ygon
by
its
nu
mbe
r of
sid
es.T
hen
cla
ssif
y it
as
con
vex
or c
onca
vean
dre
gula
ror
not
reg
ula
r.
a.b
.c.
pen
tag
on
,co
nvex
,q
uad
rila
tera
l,q
uad
rila
tera
l,co
nvex
,re
gu
lar
con
cave
,no
t re
gu
lar
no
t re
gu
lar
3.W
hat
is
anot
her
nam
e fo
r a
regu
lar
quad
rila
tera
l?a
squ
are
4.M
atch
eac
h p
olyg
on i
n t
he
firs
t co
lum
n w
ith
th
e fo
rmu
la i
n t
he
seco
nd
colu
mn
th
at c
anbe
use
d to
fin
d it
s pe
rim
eter
.(s
repr
esen
ts t
he
len
gth
of
each
sid
e of
a r
egu
lar
poly
gon
.)
a.re
gula
r do
deca
gon
ivi.
P�
8s
b.
squ
are
viii
.P�
6s
c.re
gula
r h
exag
onii
iii.
P�
a�
b�
c
d.
rect
angl
ev
iv.
P�
12s
e.re
gula
r oc
tago
ni
v.P
�2�
�2w
f.tr
ian
gle
iiivi
.P�
4s
Hel
pin
g Y
ou
Rem
emb
er
5.O
ne
way
to
rem
embe
r th
e m
ean
ing
of a
ter
m i
s to
exp
lain
it
to a
not
her
per
son
.H
ow w
ould
you
exp
lain
to
a fr
ien
d w
hat
a r
egu
lar
poly
gon
is?
Sam
ple
an
swer
:A
reg
ula
r p
oly
go
n lo
oks
th
e sa
me
no
mat
ter
wh
at
par
t yo
u lo
ok
at.T
he
sid
es a
re t
he
sam
e le
ng
th,a
nd
th
e an
gle
s ar
e th
e sa
me
size
.
©G
lenc
oe/M
cGra
w-H
ill36
Gle
ncoe
Geo
met
ry
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-6
1-6
Per
imet
er a
nd
Are
a o
f Ir
reg
ula
r S
hap
esT
wo
form
ula
s th
at a
re u
sed
freq
uen
tly
in m
ath
emat
ics
are
peri
met
er a
nd
area
of
a re
ctan
gle.
Per
imet
er:
P�
2 ��
2wA
rea:
A�
�w,w
her
e �
is t
he
len
gth
an
d w
is t
he
wid
th
How
ever
,man
y fi
gure
s ar
e co
mbi
nat
ion
s of
tw
o or
mor
e re
ctan
gles
cre
atin
gir
regu
lar
shap
es.T
o fi
nd
the
area
of
an i
rreg
ula
r sh
ape,
it h
elps
to
sepa
rate
the
shap
e in
to r
ecta
ngl
es,c
alcu
late
th
e fo
rmu
la f
or e
ach
rec
tan
gle,
then
fin
dth
e su
m o
f th
e ar
eas.
Fin
d t
he
area
of
the
figu
re a
t th
e ri
ght.
Sep
arat
e th
e fi
gure
in
to t
wo
rect
angl
es.
A�
�wA
1�
9
2A
2�
3
3�
18�
9
18�
9�
27
Th
e ar
ea o
f th
e ir
regu
lar
shap
e is
27
m2 .
Fin
d t
he
area
an
d p
erim
eter
of
each
irr
egu
lar
shap
e.
1.2.
3.4.
For
Exe
rcis
es 5
–8,f
ind
th
e p
erim
eter
of
the
figu
res
in E
xerc
ises
1–4
.
5.6.
7.8.
9.D
escr
ibe
the
step
s yo
u u
sed
to f
ind
the
peri
met
er i
n E
xerc
ise
1.S
ee s
tud
ents
’wo
rk.
48 f
t44
cm
96 m
17 in
.
A�
90 f
t2P
�46
ft
9 ft
2 ft
3 ft
7 ft
6 ft 4 ft
A�
40 c
m2
P�
44 c
m
8 cm
4 cm
2 cm
2 cm
4 cm
4 cm
6 cm
4 cm
A�
320
m2
P�
96 m
9 m
26 m
6 m
13 m
7 m
12 m
A�
12 in
2
P�
20 in
.
2 in
.
4 in
.4
in.
1 in
.
9 m
3 m
1
25
m
2 m
9 m
3 m
5 m
2 m
Exam
ple
Exam
ple
Answers (Lesson 1-6)
© Glencoe/McGraw-Hill A20 Glencoe Geometry
Chapter 1 Assessment Answer Key Form 1 Form 2APage 37 Page 38 Page 39
(continued on the next page)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
D
A
B
C
D
A
A
C
A
B
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
B
A
D
D
B
C
A
D
D
B
12 yd
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
B
D
C
A
B
C
C
C
A
B
© Glencoe/McGraw-Hill A21 Glencoe Geometry
Chapter 1 Assessment Answer KeyForm 2A (continued) Form 2BPage 40 Page 41 Page 42
An
swer
s
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
C
A
C
C
B
D
B
A
B
A
32
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
B
D
D
A
C
B
A
D
C
B
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
A
B
D
C
D
A
B
C
C
C
64
© Glencoe/McGraw-Hill A22 Glencoe Geometry
Chapter 1 Assessment Answer KeyForm 2CPage 43 Page 44
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Sample answer:DE���
A, B, C
AB���
Sample answer:D, E, C
6.3 cm
0.5 mm
7.3 cm
27 cm
3 in.
�58���32
�, ��52
��
(�1, �3)
15 � 5�5�
x � 8, y � 7
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
64°, acute
6
5
11
108
68
6
hexagon, convex,regular
174
35
21
length � 11;width � 4
© Glencoe/McGraw-Hill A23 Glencoe Geometry
Chapter 1 Assessment Answer KeyForm 2DPage 45 Page 46
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Sample answer:TU���
Sample answer:T, U, V
RS���
Sample answer:X, Y, Z
1�12
� in.
�14
� in.
5.7 cm
17 cm
7
�65�
�3�12
�, 0�
(1, �1)
10 � �90� � �250�or 10 � 8�10� �
35.3 units
2
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
135°, obtuse
6
6
7
122
32
9
pentagon,convex, regular
185
51
68
10, 18, 9
© Glencoe/McGraw-Hill A24 Glencoe Geometry
Chapter 1 Assessment Answer KeyForm 3Page 47 Page 48
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
planes ABCD,BFCE, FBA, CDE,
and plane P orADEF
DC��� or BC���
AE���
1�14
� in.
�18
� in.
12.3 cm and 19.3 cm
6
8
�20� or 2�5� � 4.5
��2, ��12
��,(�4, �1.5)
y � 2, y � �4
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
3
15.5 � x � 8
27
36
8
8.5
quadrilateral,concave, irregular
9 � �5� � 3�10�� 20.7
39
square: 9,triangle: 12
x
y
O
BC
D
A
Chapter 1 Assessment Answer KeyPage 49, Open-Ended Assessment
Scoring Rubric
© Glencoe/McGraw-Hill A25 Glencoe Geometry
Score General Description Specific Criteria
• Shows a thorough understanding of concepts involvingspecial angle relationships, classification of angles,distance formula, regular polygons, angle bisectors, andperimeters.
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Graphs and figures are accurate and appropriate.• Goes beyond requirements of some or all problems.
• Shows an understanding of the concepts involving specialangle relationships, classification of angles, distanceformula, regular polygons, angle bisectors, and perimeters.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Graphs and figures are mostly accurate and appropriate.• Satisfies all requirements of problems.
• Shows an understanding of most of the concepts involvingspecial angle relationships, classification of angles,distance formula, regular polygons, angle bisectors, andperimeters.
• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Graphs and figures are mostly accurate.• Satisfies the requirements of most of the problems.
• Final computation is correct.• No written explanations or work is shown to substantiate
the final computation.• Graphs and figures may be accurate but lack detail or
explanation.• Satisfies minimal requirements of some of the problems.
• Shows little or no understanding of most of the conceptsinvolving special angle relationships, classification ofangles, distance formula, regular polygons, anglebisectors, and perimeters.
• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Graphs and figures are inaccurate or inappropriate.• Does not satisfy requirements of most problems.• No answer may be given.
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
4 SuperiorA correct solution that is supported by well-developed, accurateexplanations
An
swer
s
© Glencoe/McGraw-Hill A26 Glencoe Geometry
Chapter 1 Assessment Answer KeyPage 49, Open-Ended Assessment
Sample Answers
1.
points A, B, and C
2a. After drawing a line on a coordinategrid, students should label two pointson the graph D and G.
b. The students should use either thePythagorean Theorem, the DistanceFormula, or the Midpoint Formula todetermine the distance between pointsD and G.
c. Using the Midpoint Formula and theknown coordinates for points D(x1, y1)and G(x2, y2), the coordinates of pointH(x, y) can be found by solving for x
and y in �x �
2x1
� � x2 and �y �
2y1
� � y2.
3a. The student draws a rectangle, labelsthe vertices W, X, Y, and Z, labels thewidth with a variable, such as x, andthe length in terms of that variable,3x � 5.
b. An expression for the perimeter, where x is the width, would be either 2(3x � 5) � 2x or 8x � 10.
c. Solving 58 � 8x � 10 for x, the width isfound to be 6 mm. To check that thisanswer is correct, use the value of thewidth to determine the length, 23. Thesum of all four sides, 23 � 23 � 6 � 6,should equal 58.
d. After using a ruler to draw a segmentthat is 23 mm long, students shouldlabel the endpoints P and Q.
e. A measurement of 23 mm for P�Q� isaccurate to within 0.5 mm. So, ameasurement of 23 mm could be 22.5 to23.5 mm.
4a. After drawing an acute angle, the studentlabels the vertex B and point A on oneray and point C on the other ray. Thenthe student uses a protractor to find themeasure of �ABC. The student lets themeasure of �ABC equal (6x � 1) andsolves for x.
b. To find the measure of an angle that iscomplementary to �ABC, you wouldsubtract m�ABC from 90.
c. To find the measure of an angle that issupplementary to �ABC, you wouldsubtract m�ABC from 180.
5a.
b. If RS��� is an angle bisector, then m�TRSand m�SRU must be equal. Therefore,solve 4x � 6 � 8x � 6 for x.4x � 6 � 8x � 66 � 6 � 8x � 4x Add 6 and subtract 4x from
each side.
12 � 4x Combine like terms.
3 � x Divide each side by 4.
c. When x � 7.5, m�TRS � 4(7.5) � 6 andm�SRU � 8(7.5) � 6. Simplifying eachexpression results in m�TRS � 36 andm�SRU � 8(7.5) � 6 � 54. Since thesum of the two measures is 90, RU��� andRT��� must be perpendicular.
U
S
T
R
(4x � 6)�
(8x � 6)�
R
s
BC
A
In addition to the scoring rubric found on page A25, the following sample answers may be used as guidance in evaluating open-ended assessment items.
© Glencoe/McGraw-Hill A27 Glencoe Geometry
Chapter 1 Assessment Answer KeyVocabulary Test/Review Quiz 1 Quiz 3Page 50 Page 51 Page 52
An
swer
s
Quiz 2Page 51
Quiz 4Page 52
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
perpendicular
complementary
angle
midpoint
vertical angles
angle bisector
supplementary
adjacent angles
acute angle
congruent
Sample answer: Sincethe measuring tool is
divided into �12
�-inch
increments, themeasurement isprecise to within
�14
� inch.
Sample answer: Point
M is between points Pand Q only if P, Q, and
M are collinear andPM � MQ � PQ.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
RS���, or RU��� or SU���
point Spoints R, S, U or
points T, S, V
1�14
� in.
�18
� inch
8.9 cm
3
33 in.
4
C
1.
2.
3.
4.
5.
(4, 7)(3, �2)
14
40
B
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
TobtuseU or V
23Sample answer:
�TSU and �USV�TSU and �WSP or
�TSP and �USW
19
12
25
B
1.
2.
3.
4.
5.
Sample answer:
14 m
86 units
The perimeter isdoubled.
4
© Glencoe/McGraw-Hill A28 Glencoe Geometry
Chapter 1 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 53 Page 54
Part I
Part II
6.
7.
8.
9.
10.
�37�
��12
�, �1�(0, 3)
3
74 units
1.
2.
3.
4.
5.
B
C
B
C
D
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
A, C, and E or B, D, and F
C
3 cm
10 mm
26 units
B (�7, 1)
vertex: N; sides: NJ���
and NK���; 90�; right
vertex: N; sides: NK���
and NH���; 100�; obtuse
�AFB and �FCD or �EFG and �FCD or
�CFD and �CDG
�AFE and �BFD
�AFB or �EFG
7
quadrilateral;concave; irregular
10 � �50� � 17.1 units
18 cm
© Glencoe/McGraw-Hill A29 Glencoe Geometry
Chapter 1 Assessment Answer KeyStandardized Test Practice
Page 55 Page 56
An
swer
s
Chapter 1 Assessment Answer KeyStandardized Test Practice
Page 55 Page 56
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
E F G H
A B C D
E F G H
A B C D 11. 12.
13. 14.
15.
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
16.
17.
18.
20 units
81.5 units
21 units
2 8 . 9
1 1
5 5
2 0