g eometry p resentation #1 b uilding b locks of g eometry & c lassifying a ngles a pril 22, 2013...
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GEOMETRY PRESENTATION #1BUILDING BLOCKS OF GEOMETRY & CLASSIFYING ANGLESAPRIL 22, 2013MATH BLOCK 4Learning Objective:
Identify and describe geometric figures
Identify angles and angle pairs
Warm UpWhat geometry term might you associate with each object?
1. one edge of a cardboard box 2. the floor
3. the tip of a pen
line segment or line
plane or rectangle
point
Vocabulary
pointlineplanerayline segmentcongruent
A point is an exact location. It is usually represented as a dot, but it has no size at all.
• A point AUse a capital letter to namea point.
A line is a straight path that extends without end in opposite directions.
A number line is an example of a line.
Helpful Hint
XY, or YX, or lUse two pointson the line or a lowercase letter to name a line.
X Y
l
A plane is a Flat surface that Has no thickness and extends forever.
plane QRSUse three pointsin any order, noton the same line,to name a plane.
A coordinate plane is an example of a plane.
Helpful Hint
Q
R
S
Identify the figures in the diagram.
Additional Example 1: Identifying Points, Lines, and Planes
DE
F
A. three points
B. two lines
C. a plane
D, E, and F
DE, DF
plane DEF
Choose any two points on a line to name the line.Choose any three points, not on the same line, in any order.
Check It Out: Example 1
HI
A. four points
B. two lines
C. a plane
H, G, I, and F
IH, HF
plane IGF
Identify the figures in the diagram.
G
Choose any two points on a line to name the line.Choose any three points, not on the same line, in any order.
F
A ray is a part of a line.It has one endpoint andextends foreverone direction.
GHName the endpointfirst when naminga ray.
A line segment is part of a line. or a raythat extends from oneendpoint to another.
LM, or MLUse the endpointsto name a line segment.
L M
HG
Identify the figures in the diagram.
Additional Example 2: Identifying Line Segments and Rays
M N
O
A. three rays
B. two line segments
MN, NM, MO
MN, MO
Name the endpoint of a ray first.
Use the endpoints in any order to name a segment.
Identify the figures in the diagram.
C
AB
D
Check It Out: Example 2
A. three rays
B. three line segments
BC, CA, BD
BA, CA, BD
Name the endpoint ofa ray first.
Use the endpoints in any order to name a segment.
Figures are congruent if they have the same shape and size. Line segments are congruent if they have the same length.
You can use tick marks to indicate congruent line segments. In the triangle below, line segments AB and BC are congruent.
Identify the line segments that are congruent in the figure.
Additional Example 3: Identifying Congruent Line Segments
AB CD
AC BD
BF DF EC AE
One tick mark
Two tick marks
Three tick marks
The symbol means “is congruent to.”
Reading Math
Check It Out: Example 3
Identify the line segments that are congruent in the figure.
AB AC
BC DE
BD CE
One tick mark
Two tick marks
Three tick marks
A
B C
D E
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
Lesson Quiz
Identify the figures in the diagram.
1. lines
2. planePossible answer: plane ABG
3. three rays
Possible answer: GA, GB, GC
4. four line segments Possible answer: AG, AD, DG, BG
5. Identify the line segments that are congruent in the figure.
AD, BE, CF
AG GD, GB GE
1. Identify the lines in the diagram.
A.
B. AB, AE
C.
D.
Lesson Quiz for Student Response Systems
2. Identify a plane in the diagram.
A. plane AFD
B. plane EFC
C. plane ABC
D. plane BGF
Lesson Quiz for Student Response Systems
3. Identify three rays in the diagram.
A.
B.
C.
D.
Lesson Quiz for Student Response Systems
4. Identify the line segments that are congruent in the figure.
A.
B.
C.
D.
Lesson Quiz for Student Response Systems
Vocabularyanglevertexright angleacute angleobtuse anglestraight anglecomplementary anglessupplementary angles
An angle is formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex.
Angles are measured in degrees (°).
A
CB
1
Vertex
An angle’s measure determines the type of angle it is.
A right angle is an angle that that measures exactly 90°. Thesymbol indicates a right angle.An acute angle is an anglethat measures less than 90°.
An obtuse angle is an anglethat measures more than 90°but less than 180°.
A straight angle is an anglethat measures exactly 180°.
Tell whether each angle is acute, right, obtuse or straight.
Additional Example 1: Classifying Angles
A. B.
obtuse angle acute angle
You can name this angle ABC, CBA, B, or 1.
Reading Math
A •
B • • C
1
Check It Out: Example 1
Tell whether each angle is acute, right, obtuse, or straight.
A. B.
straight angle acute angle
If the sum of the measures of two angles is90°, then the angles are complementary angles. If the sum of the measures of twoangles is 180°, then the angles are supplementary angles.
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2A: Identifying Complementary and Supplementary Angles
OMP and PMQ
Since 60° + 30° = 90°, PMQ and OMP are complementary. O
N
P Q
RM
To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mOMP = 60°.
If the angle you are measuring appears obtuse, then its measure is greater than 90°. If the angle is acute, its measure is less than 90°.
Reading Math
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2B: Identifying Complementary and Supplementary Angles
NMO and OMR
mNMO = 15° and mOMR = 165°
O
N
P Q
RM
Since 15° + 165° = 180°, NMO and OMR are supplementary.
Read mNMO as “the measure of angle NMO.”
Reading Math
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2C: Identifying Complementary and Supplementary Angles
8-2
PMQ and QMR
O
N
P Q
RM
Since 30° + 75° = 105°, PMQ and QMR are neither complementary nor supplementary.
To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mQMR = 75°.
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2A
BAC and CAF
mBAC = 35° and mCAF = 145°
C
B
D
E
FA
Since 35° + 145° = 180°, BAC and CAF are supplementary.
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2B
CAD and EAF
Since 55° + 35° = 90°, CAD and EAF are complementary.
C
B
D
E
FA
To find mCAD start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° - 35° = 55°. mEAF = 35°.
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2C
BAC and EAF
mBAC = 35° and mEAF = 35°
C
B
D
E
FA
Since 35° + 35° = 70°, BAC and EAF are neither supplementary nor complementary.
Angles A and B are complementary. If mA is 56°, what is the mB?
Additional Example 3: Finding Angle Measures
Since A and B are complementary, mA + mB = 90°.
mA + mB = 90°
56° + mB = 90°
– 56° – 56°
mB = 34°
Substitute 56° for mA.
Subtract 56° from both sides.
The measure of B = 34°.
Angles P and Q are supplementary. If mP is 32°, what is the mQ?
Check It Out: Example 3
Since P and Q are supplementary, mP + mQ = 180°.
mP + mQ = 180°
32° + mQ = 180°
– 32° – 32°
mQ = 148°
Substitute 32° for mP.
Subtract 32° from both sides..
The measure of Q = 148°.
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
Lesson Quiz: Part ITell whether each angle is acute, right, obtuse, or straight.
1. straight
obtuse2.
Lesson Quiz: Part IIUse the diagram to tell whether the angles are complementary, supplementary, or neither.
3. AZB and BZC neither
4. BZC and CZD complementary
5. Angles M and N are supplementary. If mM is 117°, what is mN? 63°
1. Identify the type of the given angle.
A. acute
B. obtuse
C. right
D. straight
Lesson Quiz for Student Response Systems
2. Identify the type of the given angle.
A. acute
B. obtuse
C. right
D. straight
Lesson Quiz for Student Response Systems
3. Use the diagram to identify the type of the given pair of angles. mAOB and mBOD
A. complementary
B. supplementary
C. right
D. none
Lesson Quiz for Student Response Systems
4. Angles A and B are complementary. If mA is 36°, what is mB?
A. 54°
B. 90°
C. 126°
D. 144°
Lesson Quiz for Student Response Systems
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