geometry teacher’s edition - assessment - ck-12...

Geometry Teacher’s Edition - Assessment

CK-12 Foundation

January 20, 2010

http://www.ck12.org

CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbookmaterials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the “FlexBook,” CK-12 intends to pioneer the generationand distribution of high quality educational content that will serve both as core text as wellas provide an adaptive environment for learning.

Copyright ©2009 CK-12 Foundation

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Contents

1 Geometry TE - Assessment 5

1.1 Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.3 Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.4 Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

1.5 Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

1.6 Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

1.7 Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

1.8 Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

1.9 Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

1.10 Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

1.11 Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

1.12 Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

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Chapter 1

Geometry TE - Assessment

1.1 Chapter 1

Quiz: Points, Lines, and Planes

Name:________________________Hour:______Date:______________1. Describe the following diagram as completely as possible.

2. Why are point, line, and plane considered undefined terms? What does being “undefined”allow for these terms?

3. Draw a picture of two intersecting planes and darken the intersection. What type ofgeometric figure results from this intersection?

4. Draw a sketch of the following information: −−→CD intersecting ←→AB at point Q.

5. What is the best way to describe the path taken by air from Houston, Texas to Min-

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neapolis, Minnesota?

Answers: Points, Lines, and Planes

1. ←→CB intersects ←→HG at point I.

2. Sample: There is no precise way to define these words. Leaving them undefined allowsthe words to be recognizable but use them in other definitions, such as collinear.

3. Sample diagram is shown below. The resulting figure is a line.

http://commons.wikimedia.org/wiki/File:Interseting_planes.svg

4. Sample is shown below

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5. Line segment

Quiz: Segments, Distances, Rays, and Angles

Name:________________________Hour:______Date:______________1. Marcia took a road trip with some friends. When she left, her odometer read 65, 253 miles.When she returned, her odometer read 69, 107 miles. How many miles did Marcia drive?

2. Graph A = (1, 2) and B = (−6, 2) on the graph below. Find AB.

3. Find the measure of ∠TUV below.

4. Suppose in the drawing below, m∠SAD = 52◦ and m∠SAT = 64◦. What can youconclude using the Angle Addition Property?

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5. Using the diagram below list all pairs of equal angles.

6. Match the each of the following terms with its correct definition.

a. Straight Angle

b. Right Angle

c. Acute Angle

d. Obtuse Angle

I. 90◦ < m∠A < 180◦

II. m∠A = 180◦

III. 0◦ < m∠A < 90◦

IV. m∠A = 90◦

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Answers: Segments, Distances, Rays, and Angles

1. 3, 854 miles

2. AB = 7 units

3. Approximately 122◦

4. m∠DAT = 116◦

5. m∠ZQY = m∠RQP ; m∠RQZ = m∠PQY6. a− 2, b− 4, c− 3, d− 1

Quiz: Segments and Angles

Name:________________________Hour:______Date:______________1. Assume AB = 10 mm and CD = 10 mm. What can you conclude about these twosegments?

2. The segment below is 12.5 cm. Find and label its midpoint, marking congruent segments.

3. Construct ∠ABC with measure 127◦. Then draw its angle bisector, labeling congruentangles.

4. Assume ∠V ∼= ∠R. Find x and the measure of each angle.

Answers: Segments and Angles

1. You can conclude AB ∼= CD

2. Answer shown below. Each segment has length 6.25 cm.

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3. Answer shown below. Bisector should divide main angle into 63.5◦ sections.

4. x = 9; m∠V = m∠R = 42◦

Quiz: Angle Pairs

Name:________________________Hour:______Date:______________1. Describe the difference between a pair of complementary angles and a pair of supplemen-tary angles.

2. True or False. Supplementary angles always form a linear pair.

3. Using the diagram below, list the following:

a. A pair of vertical angles

b. A linear pair

c. A pair of complementary angles

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4. Assume the following diagram. m∠TMK = 55◦.a. Find m∠TMHb. Find m∠JMH

5. Using the above diagram, now suppose m∠TMK = 11z + 3 and m∠JMH = 2z + 30.Find m∠TMK.

Answers: Angle Pairs1. Sample: Supplementary angles have a sum of 180 degrees while complementary angleshave a sum of 90 degrees. Supplementary angles form a straight angle and complementaryangles form a right angle.

2. False, a counter example can be drawn with two non-adjacent angles with a sum of180 degrees.

3. Samples:

a. ∠ECA & ∠BCDb. ∠EAC & ∠ECBc. ∠ECF & ∠FCB4. m∠TMK = 125,m∠JMH = 555. 36◦

Quiz: Classifying PolygonsName:________________________Hour:______Date:______________1. Label the following triangle as completely as possible.

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2. Draw an acute isosceles triangle.

3. Can the following be classified as a polygon? Explain your answer.

4. Calculate BC

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Answers: Classifying Polygons

1. Obtuse triangle. It cannot be assumed an isosceles because there are no tic marks showingequal lengths.

2. Sample shown below.

3. Yes, the figure can be classified as a polygon. It is the union of line segments meeting atendpoints. It is a closed figure with no curved sides.

4. BC =√

34 units

Test Basics of Geometry

Name:________________________Hour:______Date:______________1. Brad lives 7 miles north from Kevin. Corey lives 8 miles west of Kevin.

a. Show possible locations of Brad, Kevin, and Corey on a coordinate grid.

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b. How far does Brad live from Corey?

2. Underline the undefined term(s) in the following definition of coplanar. Two or morelines are coplanar if they share the same plane.

3. Suppose M is the midpoint of AB. What is AB if MB = 6 miles?

4. Aaron visited his friend, Crystal. She explained to him how her town, Shelbyville, wasset up.

a. Using the following information, draw a map of Shelbyville.

• Main Street is parallel to Second Avenue.• Second Street is parallel to Washington Avenue.• Jackson Street is perpendicular to Washington Avenue.

b. What must be true about this map?

Use the figure for questions 5 - 7.

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5. Name three collinear points.

6. Name four coplanar points.

7. What is the intersection of ←→HI and plane J?

8. Why is it useful to have more than one way to name an angle?

9. Suppose ∠BJM = 3x+4 andMKD = 5x−10. ∠BJM and ∠MKD are complementary.Solve for x and determine the measurement of each angle.

10. Explain, using one of the postulates you have learned, why surveyors use three-leggedstands for their instruments.

11. Determine the distance between (−4, 7) and (14, 7).

12. Suppose C is the midpoint of AB. Find AC, CB, and AB.

13. Highway mile markers give the mileage from one end of a state to its opposite end. InMichigan, US127 runs from the Ohio/Michigan state line to Clare. If Jackson is located atmile marker 43 and Alma is located at mile marker 118, how far apart are these two cites?

14. Find the measure of this angle and classify it as obtuse, acute, right, or straight.

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15. Draw and label a figure to fit the following information: two angles that are supplemen-tary, adjacent, and equal measure.

16. Is the following figure considered a polygon? Explain your reasoning. If it is a polygon,name it appropriately.

17. Estimate the angle formed by the hour and minute hands of a clock at 9:35.

Answers: Test Basics of Geometry

1. See below

2. Two or more lines are coplanar if they share the same plane.

3. AB = 12 miles

4. See below

5. E,G, F

6. E,G, F, J

7. G

8. Sample: The intersection formed by two lines or segments results in four angles, so by

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using all three points when naming an angle, you can be very specific regarding the angleyou are referencing

9. x = 12; m∠BJM = 40; m∠MKD = 5010. Sample: The ______ Postulate states that three points determine a plane. The legsof the tripod represent three points and the ground represents the plane. Adding a fourthleg (point) often makes the chair or stand wobbly.

11. 18 units

12. x = 5; AC = 15, BC = 15, AB = 30

13. 75 miles

14. 95 degrees

15. See below

16. Sample Yes, the figure is a polygon because it is a closed figure made with the union ofline segments. It’s specific name is a nonconvex (concave) heptagon.

17. 60 degrees

Standardized Test Prep Basics of GeometryName:________________________Hour:______Date:______________Use the diagram to answer questions 1 - 3.

1. How many segments are in the figure?

A. 1

B. 4

C. 6

D. 10

E. 14

2. Which ray is opposite to −−→DE?

A. −−→BE

B. −−→CB

C. −→AE

D. −−→DE

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E. −−→DB

What is another name for −−→BD?

A. −−→DE

B. −−→BE

C. −−→CB

D. −→CA

E. none of the above

4. Which figure could be the intersection of two planes?

A. line

B. ray

C. point

D. segment

E. A & B only

5. NU has endpoints (−8, 1) and (−8,−8). Which other point must lie on the segment?

A. (16, 7)

B. (0,−7)

C. (8, 3)

D. (−8, 3)


6. Points A, B, and C are collinear with A between B and C. Which of the following mustbe true?

A. AB + BC = AB

B. BC − AB = AC

C. AB −BC = AB

D. A and B only

E. A and C only

7. Two angles are adjacent and supplementary. What is the measure of each?

A. 90

B. 180

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C. 45

D. 60

E. cannot be determined

8. A triangle has three equal sides. What can you determine about its angles?

A. The measures are 30◦

B. The measures are 60◦

C. cannot be determined

9. ∠K and ∠F are vertical angles. Their sum is 146◦. What is m∠K?A. 73

B. 36.5

C. 144

D. 62


10. The measure of an angle is 22 less than the measure of its supplement. What is themeasure of the angle?

A. 101

B. 79

C. 148

D. 123


11. Which term is a geometric undefined term?

A. Point

B. line

C. plane

D. A and B only

E. all of the above

12. Which best describes the figure below?

A. Scalene acute triangle

B. equilateral acute triangle

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C. Isosceles obtuse triangle

D. scalene obtuse triangle

E. isosceles acute triangle

Use the diagram below for questions 13 - 18. Assume ∠C forms a right angle and AB∥JK.

13. Which angles represent a linear pair?

A. ∠AEF & ∠BEGB. ∠FEH & ∠HEBC. ∠ICD & ∠HEBD. ∠JCH ∠DCEE. none of the above

14. ∠AEF and ∠BEG are _________.A. Supplementary

B. complementary

C. equivalent

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D. Vertical angles

E. both C and D

15. ∠JCD has measure of _____.A. 90

B. 85

C. 180

D. 100


16. Which postulate allows for the statement ∠FEH + ∠HEB = ∠FEB?A. Segment Addition Property

B. Angle Addition Property

C. Midpoint Postulate

D. Vertical Angles Postulate

17. Suppose m∠BEG = 42. What is the measure of ∠AEG?A. 138

B. 90

C. 42

D. 48


18. E is the midpoint of AC. What does HI represent?

A. Bisector

B. midpoint

C. perpendicular

D. both A and C


Answers: Standardized Test Prep Basics of Geometry

1. D

2. E

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3. B

4. A

5. D

6. B

7. A

8. B

9. A

10. B

11. E

12. D

13. D

14. E

15. C

16. B

17. A

18. D

1.2 Chapter 2

Quiz: Inductive Reasoning and Conditionals

Name:________________________Hour:______Date:______________1. Find the next two terms in the following pattern: 2.4, 2.45, 2.456, 2.4567, . . .

2. Show by providing a counterexample that the following statement is false. “If you areover 16, then you can drive legally.”

3. Consider the following conditional. Underline the hypothesis with one line and theconclusion with two lines. “If a quadrilateral is a square, then it has four right angles andfour congruent sides.”

4. Consider the following conditional. “If an animal is a zebra, then it is a mammal.”

a. Write its inverse.

b. Write its converse.

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c. Write its contrapositive.

d. Assuming the original statement is true, which of the above (a− c) is also true?

5. Consider the following biconditional. “A triangle is scalene if and only if it has no sidesof equal length.”

a. Separate this into its two respective statements.

b. Do you think this is a true statement? Explain your reasoning.

Answers: Inductive Reasoning and Conditionals1. 2.45678, 2.456789

2. Sample: You could be 80 and have your license revoked due to vision problems

3. “If a quadrilateral is a square, then it has four right angles and four congruent sides.”

4. a. If an animal is not a zebra, then it is not a mammal.

b. If an animal is a mammal, then it is a zebra.

c. If an animal is not a mammal, then it is not a zebra.

d. The contrapositive is true

5. a. If a triangle is scalene, then it has no sides of equal length. If a triangle has no sidesof equal length, then it is scalene.

b. Yes, this fits the definition of a scalene triangle.

Quiz: Deductive Reasoning and Algebraic PropertiesName:________________________Hour:______Date:______________1. The following series of statements were created by the author Lewis Carroll, most notedfor Alice in Wonderland. What can you conclude using these clues?

a. Colored flowers are always scented.

b. I dislike flowers that are not grown in the open air.

c. No flowers grown in the open air are colorless.

2. Complete the following truth table:

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Table 1.1: (continued)

P : p p∧ : p

Table 1.1:

P : p p∧ : p

3. The following is the work shown to solve for variable x. Complete each step with itsappropriate property.

a. 6x + 32 = 16x + 98 Given

b. 6x + 32 +−6x = 16x + 98 +−6x ____________________

c. 32 = 10x + 98 ____________________

d. 32 +−98 = 10x +−98 ____________________

e. 56 = 10x

f. 5610

= 10x10____________________

g. 5.6 = x ____________________

4. Match the correct statement to its property

a. If 3x = 16, then 16 = 3x

b. 16 = 16

c. If a = 3 and 3 = b, then a = b.

d. ∠C ∼= ∠Ce. If 14a = 12, then 14a + 6 = 18.

Reflexive Property of Equality

Reflexive Property of Congruence

Symmetric Property of Equality

Symmetric Property of Congruence

Transitive Property of Equality

Transitive Property of Congruence

Addition Property of Equality

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Answers: Deductive Reasoning and Algebraic Properties

1. I like scented flowers.

2.

P : p p∧ : pT F F

F T F

3. b. Addition Property of Equality

c. Simplification (Adding Like Terms)

d. Addition Property of Equality

f. Multiplication Property of Equality (Division Prop of Equality)

g. Simplification (Reflexive Property of Equality)

4. a. Symmetric Property of Equality

b. Reflexive Property of Equality

c. Transitive Property of Equality

d. Reflexive Property of Congruence

e. Addition Property of Equality

Quiz: Diagrams, Two-Column Proofs, and Congruence The-orems

Name:________________________Hour:______Date:______________1. Write the following paragraph proof of the Congruent Supplements Theorem into two-column form. Include a sketch of the theorem. Congruent Supplements Theorem: Iftwo angles are supplements of the same angle (or of congruent angles), then thetwo angles are congruent.

Using the definition of supplementary angles, m∠1 + m∠2 = 180 and m∠2 + m∠3 = 180.Applying the substitution property of equality, m∠1 + m∠2 = m∠2 + m∠3. The AdditionProperty of Equality allows us to subtract m∠2 from each side of the equation. Therefore,m∠1 = m∠3 and ∠1 ∼= ∠3.2. What are some things you cannot assume when looking at a diagram?

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3. Prove the following in two-column format, “If two angles are congruent and supplementary,then each is a right angle.

4. What are the categories of reasons (justifications) used in proofs?

5. Complete the proof of the following conditional All right angles are congruent.

Table 1.2:

Statement Reason∠M and ∠N are right angles a.m∠M = 90 and m∠N = 90 b.c. Substitution Property

Answers: Diagrams, Two-Column Proofs, and CongruenceTheorems1.

Table 1.3:

Statement Reason∠1 and ∠2 are supplementary angles Givenm∠1 + m∠2 = 180 Definition of Supplementary Anglesm∠1 + m∠2 = m∠2 + m∠3 Substitution Propertym∠1 + m∠2−m∠2 = m∠2−m∠2 + m∠3 Addition Property of Equalitym∠1 = m∠3

2. Right angles, parallel lines, perpendicular lines, and distance cannot be assumed from adiagram - you must be told by notation.

3.

Table 1.4:

Statement Reason∠A and ∠B are congruent and supplemen-tary

Given

∠A ∼= ∠B Congruent Angles Theoremm∠A + m∠B = 180 Definition of supplementary anglesm∠A + m∠A = 180 Substitution Property2 m∠A = 180; m∠A = 90 Multiplication Property of Equalitym∠A and m∠B are right angles Definition of a right angle

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Statement Reason

4. Definition, postulates, previously proved theorems

5. a. Given

b. definition of a right angle

c. ∠M ∼= ∠N

Chapter Test Reasoning and ProofName:________________________Hour:______Date:______________1. Write the following statement as a conditional: All puppies are cute.

2. If is it snowing in Ohio, then it is not summer.

a. Write the converse of this statement.

b. Is the converse true? Explain your reasoning.

3. The measure of an angle is 3m. What is the measure of its complement?

4. Given the following clues, what can you conclude (if anything)? What reasoning allowsyou to make this assumption?

a. Sonja is a freshmen.

b. Freshmen floss their teeth regularly.

5. Use a truth table to determine whether the following argument is valid:

a. If you invest in Ericon, then you will get rich.

b. You did not invest in Ericon.

c. Therefore, you did not become rich.

6. Solve the equation. Write the appropriate reasoning for each step.

11x + 43 = −23

7. What property justifies this statement: If AB = DM and AB = JK, then DM = JK.

8. Amphibians have skin that is scale-less and permeable to water.

a. Write the inverse of this statement.

b. Write the contrapositive.

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c. Write its converse.

d. Assuming the original statement is true, which of the above statements (a − c) is alsotrue?

9. Sketch a diagram that represents the given information. ∠SAP , an obtuse angle, isbisected by ←−→DM .

10. Describe the following pattern and write the next four numbers in the sequence:14, 5, 13, 4, 12, 3, . . .

11. Find a counterexample to disprove the hypothesis The sum of two irrational numbers isirrational.

12. Find x, y, and the measures of each angle in the diagram below.

13. Prove the following: If AE ∼= BE and DE ∼= BE, then AC ∼= BD

Answers: Chapter Test Reasoning and Proof

1. If an animal is a puppy, then it is cute.

2. a. If it is not summer in Ohio, then it is snowing.

b. No, it could be fall in Ohio and not snowing.

3. 90− 3m

4. Sonja flosses regularly (Law of Detachment)

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5. The argument is invalid

6. 11x+43 = −23Using the Addition Property of Equality, the equation becomes 11x = −66.Using the Division Property of Equality, the equation becomes x = −6.

7. Transitive Property of Equality

8. a. If it is not an amphibian, then its skin is not scale-less nor permeable to water.

b. If something’s skin is not scale-less nor permeable to water, then it is not an amphibian.

c. If its skin is scale-less and permeable to water, then it is an amphibian.

d. Contrapositive

9.

10. 11, 2, 10, 1

11. π +−π = 0

12. X = 35, y = 18, 126◦, 84◦

13. Using the transitive property of equality, AE ∼= DE. This means all four segments arecongruent. Using the segment addition property, AC ∼= BD

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Standardized Test Reasoning and Proof

Name:________________________Hour:______Date:______________1. What is the next number in the sequence? 2, 4, 3, 6, 5, 10, . . .

a. 15

b. 20

c. 9

d. 19

2. What is the hypothesis of the statement I’ll have pizza if it is Friday night.

a. I’ll have pizza

b. Friday

c. It is Friday night

d. None of the above

3. Which property is stated here? If x = 3 and x = 4y, then 3 = 4y.

a. Reflexive Property of Congruence

b. Symmetric Property of Equality

c. Addition Property of Equality

d. Transitive Property of Equality

4. Which term is not considered an undefined geometric term?

a. Coplanar

b. Point

c. Plane


5. Which of the following can be used to prove a statement?

a. Definitions

b. Postulates

c. Other theorems

d. all of the above

6. What is the converse of All cats have whiskers?

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a. If it is a cat, then it has whiskers

b. If it has whiskers, then it is a cat.

c. All whiskers belong to cats.

d. If it is not a cat, then it does not have whiskers.

7. Which is an instance of, If you are a band member, then you are a musician?

a. You are the bass player

b. You are a roadie

c. You are the stage manager

d. You are the busdriver

8. The measure of an angle is 6c. What is the measure of its supplement?

a. 90− 6c

b. 180− 6c

c. 45

d. cannot be determined

Answers: Standardized Test Reasoning and Proof1. C

2. C

3. D

4. A

5. D

6. B

7. A

8. B �

1.3 Chapter 3

Quiz: Parallel Lines, Angles, and TransversalsName:________________________Hour:______Date:______________

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1. Using the diagram below, list a pair of

a. Consecutive interior angles

b. Alternate interior angles

c. Corresponding angles

2. Two lines and a transversal form how many corresponding angles? What is true of theseangles if the lines are parallel?

3. Find the value of x to make lines a and b parallel.

4. Prove the following: If two lines and a transversal form same-side exterior angles thatare supplementary, then the lines are parallel.

Answers: Parallel Lines, Angles, and Transversals

1. a. Sample: ∠3 & ∠6b. Sample: ∠3 & ∠5c. Sample: ∠2 & ∠6

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2. 4 pairs of corresponding angles; they are congruent

3. x = 17

4. Suppose 2 lines are cut by a transversal forming supplementary consecutive exterior an-gles (1 and 2). ∠1 + ∠2 = 180. Angles 2 and 3 form a linear pair thus are supplementary.So ∠2 + ∠3 = 180. Using the substitution property, ∠1 = ∠2. Angles 1 and 2 are corre-sponding angles. Using the corresponding angles postulate, because corresponding anglesare congruent, the lines are parallel.

Quiz: Equations of Lines

Name:________________________Hour:______Date:______________1. Find the equation of the line passing through (−4, 8) with a slope of 3

4.

2. Line m has a slope 45. Line n has a slope of 5

4. Are these lines perpendicular, parallel, or

neither.

3. Determine the slope of the line through (3, 7) and (−1.5, 19)

4. Consider a ladder. What reasoning allows you to conclude that the rungs are eachperpendicular to one side?

5. Prove the following: If a line is perpendicular to one of two parallel lines, then it is alsoperpendicular to the other.

5. Write the symmetric statement for “is parallel to.” Is the statement true or false? Explainyour position.

6. What can you conclude using the following information? a ⊥ b, c ∥ d, b ⊥ c?

Answers: Equations of Lines

1. y = 34x + 11

2. neither

3. −83

4. The parallel to perpendicular theorem; because every rung is perpendicular to a side, therungs are parallel to each other

5. Suppose a line is perpendicular to one of two parallel lines. Then the measure of allfour angles equal 90. Because the lines are parallel, corresponding angles are congruent.Therefore, the perpendicular of one is also perpendicular to the other.

6. If l is parallel to m, then m is parallel is l. True

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7. a is parallel to d.�

Quiz: Perpendicular Transversals and Non-Euclidean Geom-etry

Name:________________________Hour:______Date:______________1. Explain why the following statement about the drawing is incorrect. a is perpendicularto c.

2. In the diagram below −−→CD ⊥ −−→BD. Find y and the measure of each angle.

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3. State the Perpendicular Transversal Theorem.

4. Prove the following statement: If ∠5 and ∠6 form a linear pair and are congruent, thenthe lines forming the angles are perpendicular.

5. Draw the taxicab circle with center (1,−3) and radius 3.

Answers: Perpendicular Transversals and Non-Euclidean Ge-ometry

1. Simply because a is perpendicular to b, you cannot assume it is also perpendicular to c.The diagram does not show this relationship.

2. y = 33, 39◦, 51◦

3. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular tothe other.

4. According to the Linear Pair Theorem, linear pair angles are supplementary. Therefore,angles 5 and 6 have a sum of 180. If they are congruent, using the substitution property,2(m∠5) = 180 and using the division property of equality, ∠5 = 90. Thus, angle 5 is a rightangle and the lines are perpendicular.

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5.

Chapter Test Parallel and Perpendicular LinesName:________________________Hour:______Date:______________1. Tell whether these two lines are skew, parallel, or perpendicular: y = 4x + 7 and y =−14

x− 3.

2. Write an equation of the line with slope 23containing point (1,−8).

3. Lines n and d are parallel. Could 40 and 40 be measurements of a pair of consecutiveinterior angles? Explain your answer.

4. Suppose lines x and y are parallel. List:

a. A pair of vertical angles

b. A pair of corresponding angles

c. A linear pair

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5. Using the diagram above and x ∥ y. Suppose m∠8 = 98◦. Find the measures of theremaining seven angles.

6. Find the value of p that makes a ∥ b.

7. A passenger in a taxi wants to see how many distinct locations he can visit if the cabtravels two blocks without turning around. Plot the possible locations on the grid below.

8. Fill in the blank: The measure of a(n) _____ angle of a triangle is equal to the sum ofthe measures of its opposite interior angles.

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9. Find the equation of the line parallel to y = 13x− 2 passing through the point (−5, 5).

10. Elm Street is to be built parallel to Main Street. What is the value of x?

Answers: Chapter Test Parallel and Perpendicular Lines

1. Perpendicular

2. y = 23x− 26

3

3. No, these angles must be supplementary

4. a. ∠5 & ∠7b. ∠4 & ∠8c. ∠5 & ∠65. Angles 2, 4, 6 all equal 98 and angles 1, 3, 5, 7 all equal 82

6. p = 70

7. Points should be located at the following coordinates: (4, 0), (5, 1), (3, 1), (2, 2), (6, 2), (3, 3), (5, 3), (4, 4)

8. Exterior

9. y = 13x + 20

3

10. 110

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Standardized Test Parallel and Perpendicular Lines

Name:________________________Hour:______Date:______________1. If two lines are cut by a transversal and corresponding angles are congruent, then thelines are _______

a. Parallel

b. Intersecting

c. Congruent


2. Two lines in which the product of slopes is −1 are _____.

a. Skew

b. Parallel

c. Perpendicular

d. None of these

2. The slope of the line formed by (−4, 5) and (8,−5) is:

a. 6/5

b. −5/6

c. 5/6

d. −6/5

A line with a zero slope is _____

a. Vertical

b. Horizontal

c. Skew

d. Oblique

5. Angles that lie on the same side of a transversal between two parallel lines are:

a. Congruent alternate interior angles

b. Supplementary consecutive interior angles

c. Congruent vertical angles

d. Congruent corresponding angles

6. Which of the following angles are alternate exterior angles?

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a. ∠1 and ∠8b. ∠1 and ∠7c. ∠2 and ∠5d. ∠4 and ∠6

7. The sum of a pair of vertical angles is 170◦. What is the measure of one angle?

a. 70

b. 100

c. 135

d. 85

8. Which is an equation for the line passing through (2,−3) with a slope of −2?

a. y = −2x + 1

b. y = −2x− 3

c. y = 2x− 3

d. x = 2

Answers: Standardized Test Parallel and Perpendicular Lines

1. A

2. C

3. B

4. B

5. B

6. B

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7. D

8. A

1.4 Chapter 4

Quiz: Triangle Sums and Congruent FiguresName:________________________Hour:______Date:______________1. MAPS ∼= TOYS.

a. Draw a sketch of this situation.

b. ∠P ∼= _____.c. SY = _____.

d. If m∠A = 64◦, then ______ = 64◦.2. Use the given coordinates to determine if △NOP ∼= △CAT .

N = (2,−2), O = (5, 1), P = (4, 8)C = (7, 5), A = (10, 8), T = (9, 13)

3. m∠1 = 32◦ and m∠3 = 44◦ of the triangle at the right. Find m∠2.

4. The sum of two exterior triangle angles is 277. What is the measurement of the remainingexterior angle?

5. Define congruent figures.

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Answers: Triangle Sums and Congruent Figures

1. a. Answers may vary; point S is shared between both figures

b. SP

c. m∠O2. No, OP ̸= AT

3. 104

4. 83

5. Geometric figures that have the same size and shape

Quiz: Triangle Congruence Using SSS, SAS, AAS, ASA, andHL

Name:________________________Hour:______Date:______________1. Are these two triangles congruent? If so, list the reasoning that allows you to make thisconclusion and write a congruency statement. If not, list the reasoning that would providea counterexample.

2. Using the diagram below, prove m∠A = m∠D.

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3. Assume AB = DE and AC = DF . What other piece(s) of information would you needto prove these triangles congruent

a. Using SSS

b. Using SAS

c. Using ASA

4. Given AC ∼= DC and ∠A ∼= ∠D = 90◦, prove △ABC ∼= △DBC.

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Answers: Triangle Congruence Using SSS, SAS, AAS, ASA,and HL1. Yes, the triangles are congruent by ASA. △DEF ∼= △CAB

2. ∠ECD ∼= ∠BCA by the Vertical Angle Theorem. △ABC ∼= △DEC by the ASACongruence Theorem. m∠A = m∠D by the CPCT .3. a. BC = EF

b. m∠A = m∠Dc. m∠A = m∠D and m∠C = m∠F4. BC ∼= BC by the Reflexive Property of Equality. △ABC ∼= △DEC by the Hypotenuse-Leg Congruence Theorem.

Quiz: Constructions, Isosceles Triangles, and Congruent Trans-formationsName:________________________Hour:______Date:______________1. List two types of congruent transformations.

2. Consider isosceles △JMK with vertex angle 102◦. Find the measurement of the baseangle.

3. Are isosceles triangles always obtuse? Explain your reasoning.

4. Construct an equilateral triangle with side AB.

5. The measure of an exterior angle of an isosceles triangle is 110◦. What are the possibleangles measures of the triangle? Explain your thought process.

6. Rotate ABCD 270◦ counterclockwise.

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Answers: Constructions, Isosceles Triangles, and CongruentTransformations

1. Reflections and rotations

2. 39

3. No, 50 + 50 + 80 is an example of an acute isosceles triangle

4.

5. 70, 70, 40 if the exterior angle is of the base angle, 55, 55, 70 if the exterior angle is of thevertex.

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6. The figure should have the following vertices: A′ = (−4,−4), B′ = (−2,−2), C ′ =(−2, 1), D′ = (−4, 1)

Chapter Test Congruent Triangles

Name:________________________Hour:______Date:______________1. Draw a picture to represent △DOG ∼= △MOP . Name all of the pairs of correspondingcongruent parts.

2. Draw a counterexample to the following statement: If two triangles have an AAA rela-tionship, then the triangles are congruent.

3. Construct the perpendicular bisector of JM .

4. Consider isosceles triangle △JMK. Vertex ∠K measures 112◦. Find m∠J .5. Suppose △BAD has the following angle measures: m∠B = 65,m∠A = 57.5,m∠D =57.5. What can you conclude about △BAD? What reason allows you to make your conclu-sion?

6. Which of the following does not yield a congruence transformation?

a. Rotating a chair in your room

b. Pushing your bike up the driveway

c. Enlarging a photograph

d. Your reflection in a mirror

7. Translate ABCD using the following rule: (x− 2, y + 0.5)

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8. Reflect △MNO over the y−axis.

9. Rotate △MNO 90 clockwise.

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Answers: Chapter Test Congruent Triangles

1. ∠D ∼= ∠M, ∠O ∼= ∠O, ∠G ∼= ∠P, DO ∼= MO, OG ∼= OP, DG ∼= MP2.

3.

4. 34

5. Triangle BAD is isosceles with base angles A and D by the Converse of the IsoscelesTriangle Base Angles Theorem.

6. C

7. The image should have the following coordinates: A’ = (−1, 3.5), B’ = (.5, 1), C’ =(−3,−3.25), D’ = (−1, .5)

8. The image should have the following coordinates: M ’ = (5, 5), N ’ = (−3, 2), O’ = (1, 6)

9. The image should have the following coordinates: M ’ = (5, 5), N ’ = (6, 1), O’ = (2,−3)

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Standardized Test Congruent Triangles

Name:________________________Hour:______Date:______________1. Which of the following is a congruent transformation?

a. Dilation

b. Translation

c. Reflection

d. B and C only

2. A geometric construction uses the following materials:

a. Ruler

b. Protractor

c. Pencil

d. Compass

3. Two sides and an included angle of one triangle are congruent to two sides and an includedangle of a second triangle. These triangles are congruent by:

a. ASA Congruence Theorem

c. SAS Congruence Theorem

b. SSA Congruent Theorem

d. There is no postulate

4. Which of the following is not a triangle congruence postulate?

a. SSA

B. AAA

c. ASA

d. AAS

5. The sum of two consecutive interior angles of a triangle is 104◦. The measure of theopposite exterior angle is

a. 104

b. 84

c. 65


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6. What additional information would you need to prove these triangles congruent usingASA Congruence Theorem?

a. ∠W ∼= ∠Zb. TW ∼= XZ

c. ∠T ∼= ∠Xd. V W ∼= Y Z

7. A triangle with all three segments of 4 inches is:

a. Equilateral

b. Equilangular

c. A and B

d. none of the above

8. Point K = (3, 4). What is K ′ following a translation of 3 units right and 7 units up?

a. (0,−3)

b. (0, 11)

c. (6, 11)

d. (6,−3)

9. Suppose ∠A ∼= ∠J, ∠B ∼= ∠K, ∠C ∼= ∠L. Which of the following is true?a. △ABC ∼= ∠KLJb. △ABC ∼= △JKL

c. △ABC ∼= △LKJ


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Answers: Standardized Test Congruent Triangles

1. D

2. D

3. C

4. B

5. A

6. C

7. C

8. C

9. B

1.5 Chapter 5

Quiz: Midsegments, Circumcenters, and Incenters

Name:________________________Hour:______Date:______________1. DE is a midsegment of △ABC. Find j.

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2. Draw ME with length 1.5” and construct its perpendicular bisector.

3. Construct an equilateral triangle with base length 2 cm.

4. Locate the circumcenter of triangle ABC.

Answers: Midsegments, Circumcenters, and Incenters

1. 22.5

2.

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3.

4. D is the circumcenter

Quiz: Centroids, Orthocenters, and Triangle Inequalities

Name:________________________Hour:______Date:______________1. X is the centroid of triangle ABC. Use the given information to find the value of m.BX = 4m + 5 and BR = 9m.

2. Of the four types of points we have introduced (circumcenter, incenter, centroid, and

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orthocenter), when is each type inside the triangle?

3. Sketch and label the triangle with the given information: side lengths 3 cm, 7 cm, and9 cm. Angle measures: 19◦, 43◦, and 118◦. The longest side is on the left and shortest sideis on the bottom.

4. How can you organize a triangle using the following theorem: If one side of a triangleis longer than another side, then the angle opposite the longer side is larger than the angleopposite the shorter side?

Answers: Centroids, Orthocenters, and Triangle Inequalities

1. m = 52

2. The incenter is always inside the triangle, the circumcenter is inside the triangle whenthe triangle is acute, the centroid is always inside the triangle, the orthocenter is inside thetriangle when it is acute.

3.

4. If you organize the information, the shortest side is opposite the smallest angle and thelongest side is opposite the largest angle.

Quiz: Indirect Proof

Name:________________________Hour:______Date:______________1. What is the purpose of an indirect proof?

2. Prove√

48 ̸= 6.9

3. Identify the two contradictory statements:

a. b and m are parallel

b. b and m have the same slope

c. b and m intersect

Prove: A right triangle cannot contain an obtuse angle.

Answers: Indirect Proof

1. To prove a statement by using a contradiction. Typically you use indirect proof whenyou cannot prove using a series of justifications.

2. Assume√

48 = 6.9. Then by squaring both sides, 48 = 47.61. however, this statement is

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not true. Therefore,√

48 ̸= 6.9

3. Either A and C or B and C

4. Assume a right triangle has an obtuse angle. Then by the Triangle Sum Theorem,90 + > 90 + m = 180. Simplifying the left side, you get a sum of greater than 180 degrees,which is impossible. Therefore, a right triangle cannot have an obtuse angle.

Chapter Test Relationships Within Triangles

Name:________________________Hour:______Date:______________1. List the angles of △ABC from smallest to largest. AB = 10, BC = 12, AC = 8.

2. List the sides of △MAP in order from longest to shortest. m∠MAP = 40◦,m∠PMA =110◦.

3. Choose the correct term to complete the sentence: A (centroid, median) is a segmentwhose endpoints are a vertex and the midpoint of the side opposite the vertex.

4. Fill in the blank with the correct term to complete the sentence. The ________ of atriangle is the point of concurrency of the angles bisectors of the triangle.

5. Graph △DOG with vertices D(1, 3), O(−4,−4), G(2,−4). Find the coordinates of:

a. Its circumcenter

b. Its centroid

c. Its orthocenter

6. Find the value of j. D is the midpoint of AB and E is the midpoint of BC.

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7. Locate the incenter of △ABC.

8. Explain the relationship between the circumcenter, incenter, centroid, and orthocenter inan isosceles triangle.

9. Are the following statements contradictory? Explain your position.

a. △ABC is acute

b. △ABC is scalene

10. Use indirect reasoning to prove quadrilateral ABCD cannot have four obtuse angles.

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11. Write a convincing argument that uses indirect reasoning. An obtuse cannot contain aright angle.

Answers: Chapter Test Relationships Within Triangles

1. ∠B, ∠C,∠A2. AP, MP, AM

3. Median

4. Incenter

5. a matches to D, b matches to H, and c matches to I

6. j = 22.5

7. See picture

8. All lie on the same line the median connecting the vertex and base

9. These are not contradictory. A triangle can have acute angles and different side lengths.

10. Assume ABCD has four obtuse angles. Then by the Polygonal Sum Theorem, >180 + > 180 + > 180 + > 180 = 360. However, the left side has a sum greater than360 degrees. Therefore, ABCD cannot have four obtuse angles.

11. Assume an obtuse triangle has a right angle. Then by the Triangle Sum Theorem,90 + x + y = 180. Using the Addition Property of Equality, x + y = 90. However, theAddition to Inequality Property states that x < 90 and y < 90. This means that no anglesare obtuse. Therefore, an obtuse triangle cannot have a right angle.

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Standardized Test Relationships Within Triangles

Name:________________________Hour:______Date:______________1. The point of concurrency of the angle bisectors of a triangle is called:

a. Centroid

b. Median

c. Orthocenter

d. Incenter

2. The midsegment joining a pair of sides of a triangle is _______ in relation to the thirdside.

a. Parallel to

b. Twice as long

c. Half as long

d. A and C only

3. The point of concurrency of the perpendicular bisectors of a triangle is:

a. Circumcenter

b. Median

c. Centroid


4. An altitude of a triangle can be:

a. The side of a triangle

b. Outside the triangle

c. In the interior of the triangle

d. All of the above

5. What is the negation of m ≥ 2?

a. m > 2

b. m < −2

c. m ≤ −2

d. m < 2

6. The orthocenter is the point of concurrency of:

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a. Angle bisectors

b. Medians

c. Altitudes

d. Perpendicular bisectors

Answers: Standardized Test Relationships Within Triangles

1. D

2. D

3. A

4. D

5. D

6. C

1.6 Chapter 6

Quiz: Polygonal Angles and Classifying Quadrilaterals

Name:________________________Hour:______Date:______________1. A polygon has an interior angle sum of 1080 degrees. How many sides does the polygonhave?

2. Determine the measurement of an exterior angle of a regular decagon.

3. Draw a Venn diagram relating the following: quadrilateral, trapezoid, square, kite, andrectangle.

4. True or false. A square is always a kite.

5. Find the value of g.

Answers: Polygonal Angles and Classifying Quadrilaterals

1. 8

2. 36 degrees

3. See sample below

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4. True

5. g = 112 degrees

Quiz: Parallelograms

Name:________________________Hour:______Date:______________1. Given: ABCD is a parallelogram. Prove: ∠AEB ∼= ∠DEC.

2. How do you find angle measurements in a parallelogram?

3. The measure of one interior angle of a parallelogram is 0.75 times the measure of anotherangle. Find the measure of each angle.

4. InMAPS, M = 70, A = 110, P = 110. IsMAPS a parallelogram? Explain your position.

5. List the ways to prove a quadrilateral is a parallelogram.

6. Describe how to prove ABCD is a parallelogram. Assume AD = BC.

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Answers: Parallelograms

1. Because ABCD is a parallelogram, its opposite sides are parallel and congruent. There-fore, AB ∼= DC. Diagonals in a parallelogram bisect each other, so AE ∼= CE andBE ∼= DE. By The SSS Triangle Congruence Postulate, △AEB ∼= △DEC. And bythe CPCT, ∠AEB ∼= ∠DEC.2. Opposite angles in a parallelogram are congruent and consecutive angles are supplemen-tary.

3. 77.14◦ and 102.86◦

4. MAPS is not a parallelogram. The order of the variables means A and P are consecutivevertices. These two angles are equal not supplementary.

5. By showing: the diagonals bisect each other, an opposite pair of segments are paralleland congruent, both pairs of opposite segments are parallel, both pairs of opposite segmentsare congruent, both pairs of opposite angles are congruent.

6. By the reflexive postulate, segment AC is congruent to segment AC. By the SAScongruence theorem, △DAC ∼= △BCA. Using the CPCT , AB ∼= DC. Therefore, bothpairs of opposite sides are congruent and ABCD is a parallelogram.

Quiz: Quadrilaterals and Biconditionals

Name:________________________Hour:______Date:______________1. Using the vertices, determine if ABCD is a trapezoid. A = (−2, 4), B = (3, 4), C =(−1,−5), D = (2,−5).

2. ABCD is a kite. Find m∠D.

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3. Is there enough information to classify the following figure as a square? Explain yourreasoning. You may assume JE = EL and KE = EM .

4. Using the vertices, name the figure as precisely as possible. Draw a sketch as a visual foryour answer. T = (−7, 4), I = (0, 9), P = (7, 4), S = (0, 0).

5. Can the following conditional be written as a biconditional? If so, write is as such. Ifnot, explain your reasoning. If a quadrilateral is a parallelogram, then its opposite sides arecongruent.

Answers: Quadrilaterals and Biconditionals

1. The slope of AB = 0. The slope of CD = 0. Since AB ∥ CD, ABCD is a trapezoid.

2. 67.5 degrees

3. No, using the given information, we can assume JKLM is a parallelogram. Using theproperties of a parallelogram, we can deduce all four angles are right angles. We also knowJK = ML and JM = KL, however, we do not know JK = JM .

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4. TIPS is a kite

5. Converse: If a quadrilateral has opposite sides that are congruent, then it is a parallelogram.It can be written as a biconditional. A figure is a parallelogram if and only if its oppositesides are congruent.

Chapter Test Quadrilaterals

Name:________________________Hour:______Date:______________1. Using the figure below:

a. Find the sum of interior angles

b. Find m∠BCD.

2. Determine the measurement of an exterior angle of a regular octagon.

3. Create a hierarchy or Venn diagram relating the following terms: Polygon, triangle,quadrilateral, isosceles trapezoid, parallelogram, square.

4. Fill in the blank with always, sometimes, or never: A parallelogram is _____________________a kite.

5. When can a trapezoid be considered a parallelogram?

6. What is the most specific name for the figure below?

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7. Classify the shape on the coordinate plane below.

8. Consider the following definition: An inscribed polygon is a polygon whose vertices all lieon a circle.

a. Write the converse of this conditional.

b. Write the biconditional of this definition

9. ABCD is an isosceles trapezoid with bases AD and BC. m∠D = 105◦. Find m∠B.

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10. Given ABCD is an isosceles trapezoid with bases AD and BC, and m∠D = m∠C.Prove ABCD is a rectangle.

Answers: Chapter Test Quadrilaterals

1. a. 1800

b. 150

2. 45

3.

4. Sometimes

5. A trapezoid is a parallelogram when it has two pairs of parallel sides.

6. Isosceles trapezoid

7. Slopes: AB = 1, AD = −12

, BC = −23

, CD = 1. ABCD is a trapezoid

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8. a. If a polygon’s vertices all lie on a circle, then it is an inscribed polygon

b. A polygon is inscribed in a circle if and only if all of its vertices lie on the circle

9. 75

10. Because ABCD is an isosceles trapezoid, its base angles are congruent. So ∠B ∼= ∠C.Furthermore, ∠D and ∠C are supplementary so ∠B = ∠C = ∠D = 90. ∠A and ∠B aresupplementary, therefore, ∠A = ∠B = ∠C = ∠D = 90. Therefore, ABCD is a rectangle

Standardized Test Quadrilaterals

Name:________________________Hour:______Date:______________1. Which is not true of a parallelogram?

a. The diagonals bisect each other

b. It contains one pair of parallel sides

c. Opposite angles are congruent

d. Consecutive angles are supplementary

2. A quadrilateral with four congruent angles is called:

a. Rhombus

b. Square

c. Rectangle

d. Kite

3. Which statement about kites is true?

a. It has two sets of congruent angles

b. It has one pair of parallel sides

c. Its opposite sides are congruent

d. The diagonals are perpendicular

4. The diagonal of a parallelogram bisects its angle. Which of the following must it be?

a. Square

b. Rhombus

c. Rectangle


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5. This type of figure has congruent base angles:

a. Trapezoid

b. Kite

c. Isosceles trapezoid

d. Rhombus

6. Which of the following does not always have perpendicular diagonals?

a. Trapezoid

b. Rectangle

c. Square

d. Rhombus

7. Three vertices of a kite are: A = (0, 5), B = (0,−1), C = (3,−2). Which could be thefourth vertex?

a. (0, 2)

b. (3, 1)

c. (−2, 3)

d. (3, 2)

8. Which of the following conditionals is false?

a. A parallelogram is a square if it has four congruent sides

b. A quadrilateral is a rhombus if its diagonal bisects a pair of opposite angles

c. A figure is a kite if it has two pairs of consecutive congruent sides

d. A parallelogram is a rectangle if its diagonals are congruent

Answers: Standardized Test Quadrilaterals

1. B

2. C

3. D

4. B

5. C

6. A

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7. D

8. A

1.7 Chapter 7

Quiz: Ratios and ProportionsName:________________________Hour:______Date:______________1. The measures of DEF are in the extended ratio of 2 : 4 : 5. Find the measures of eachangle.

2. Solve for b : 8b

= 57.

3. The Department of Natural Resources is doing a study on the migration of deer. Theycount 500 deer in 30 acres. Approximately how many deer are in the entire 600 acre forest?

4. 67

= x105. What are:

a. The means?

b. The extremes?

c. The value of x?

5. Two cities are 460 miles from each other. On a map, the distance between these cities is20 inches. What is the scale of the map? �

Answers: Ratios and Proportions1. 32.73, 81.82, 65.45

2. 11.2

3. 10, 000 deer

4. a. 6 and 105

b. 7 and x

c. 90

5. 23 miles per1 inch

Quiz: Similarity by AAA, SSS, SAS, and Similar PolygonsName:________________________Hour:______Date:______________

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1. An original photograph 4” by 6” is to be enlarged by a scale factor of 75%. What are thenew dimensions?

2. KIDS ∼ JOHN . List all pairs of congruent angles and a ratio of similitude.

3. TUB ∼ SAY . TU = 21 cm and AS = 4.5 cm. What is the scale factor?

4. Are these two triangles similar? Explain your reasoning.

http://commons.wikimedia.org/wiki/File:Angle-Angle_Similarity_Postulate.png

5. Why is there an SSS Congruence Theorem and an SSS Similarity Theorem?

6. Karen’s mom is 64” tall and casts a 40” long shadow. Karen is 54” tall. How long willher shadow be? �

Answers: Similarity by AAA, SSS, SAS, and Similar Poly-gons

1. 7” by 10.5”

2. ∠K ∼= ∠J,∠I ∼= ∠O, ∠D ∼= ∠H, ∠S ∼= ∠N , ratio of similitude −KI/JO3. 14

3

4. Yes, by the angle-angle similarity theorem, these are similar

5. Congruent figures are considered similar – they have congruent angle measures and theratio of similitude is 1.

6. 38.8” �

Quiz: Proportionality Relationships and Similarity Trans-formations

Name:________________________Hour:______Date:______________1. Label the following scale factors as: enlargement, contraction, rotation.

a. −12

b. 3

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c. 1.20%

d. −92

2. Suppose JOKE has the following vertices. Find the image of each under(

23x, 2

3y).J =

(0, 0), O = (−3, 6), K = (4, 12), E = (−1, 8)

3. You are building a scale model of your high school’s baseball diamond. The lengthbetween bases is 90 feet. If your scale is 1

30, what will the distance be between bases?

4. You are making photo stickers for your friends’ yearbooks. Your photograph Is 3.3” by3.3”. The printable area of the photo sticker is 1.1 inches by 1.1 inches. What is the scalefactor of the reduction?

Answers: Proportionality Relationships and Similarity Trans-formations1. a. Rotation and contraction

b. Enlargement

c. Contraction

d. Enlargement and rotation

2. J ’ = (0, 0), O’ = (−2, 4), K’ = (83, 8), E’ = (−2

3, 16

3)

3. 3 feet

4. 13

Chapter Test SimilarityName:________________________Hour:______Date:______________1. The following is a table relating the type of sandwich to the number sold.

a. What is the ratio of turkey sandwiches to pastrami on rye?

b. What is the ratio of peanut butter and jelly to all sandwiches sold?

Table 1.5:

Sandwich Amount SoldHam and Cheddar 15Turkey and Swiss 12Pastrami on Rye 8Roast Beef 7

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Sandwich Amount SoldPeanut Butter and Jelly 2Veggie Wrap 9Club Sandwich 19

2. Solve for c : 14c

= 911.

3. Is the following proportion true? Explain your answer.45

= 6490

4. Using the diagram below, find BC and list all the possible ratios of similitude.

5. True or false. All congruent figures are similar.

6. True or false. If a figure is similar, then it is also congruent.

7. Are the following triangles similar? Explain your rationale.

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8. Explain a fractal.

In questions 9 – 12, use kite ABCD below.

9. Draw the image of kite ABCD under a dilation of magnitude 1.5.

10. Prove that AB = 23∗ (A’B’)

11. Prove CD∥C ′D′.

12. Which angle has the same measurement as ∠D?

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Answers: Chapter Test Similarity

1. a. 32

b. 136

2. c ≈ 17.11

3. The following proportion is not true because 4 ∗ 90 ̸= 5 ∗ 64

4. BC = 60 units; 3045

, 4060

, 4530

.6040

, 23, 3

2

5. True

6. False

7. Yes, by the AAA Similarity Theorem

8. A fractal is an object that is self-similar, meaning that if you enlarge one piece of theobject, it looks like the whole object

9. The image should have the following coordinates A’ = (−4.5, 3), B’ = (−6, 1.5), C’ =(−3,−4.5), D’ = (−3, 1.5)

10.√

12 + 12 = 23(√

1.52 + 1.52). Both sides are approximately 1.414

11. Both lines have a slope of 3. Therefore, they are parallel

12. D’

Standardized Test Similarity

Name:________________________Hour:______Date:______________1. Which of the following is not a triangle similarity theorem?

a. HL

b. AA

c. SSS

d. SAS

2. One serving of mashed potatoes calls for 13cup milk. If one serving feeds two people, how

many cups of milk are needed for a party of 15?

a. 1 cup

b. 2 cups

c. 43cups

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d. 2.5 cups

3. If, between two figures, sides lengths are proportional and angle measures are similar,then the figures are:

a. Similar

b. Congruent

c. Neither

d. Cannot be determined

4. A rectangle is 516as wide as it is long. How wide is the rectangle if it is 4 feet long?

a. 12.8’

b. 15”

c. 1.25”

d. 1’

5. Suppose under a dilation with scale factor 54, AB = 23 cm. What is A’B’?

a. 23 cm

b. 21.75 cm

c. 18.4 cm

d. 28.75 cm

6. Which one is not a famous fractal?

a. Koch Snowflake

b. Pythagoras’ Curve

c. Sierpinski Triangle

d. Mandelbrot Set

7. −34does not represent which of the following:

a. Contraction

b. Rotation

c. Expansion


8. If a line intersects two sides of a triangle and is parallel to the third line, then it dividesthe two sides:

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a. Proportionally

b. Congruently

c. perpendicularly


Answers: Standardized Test Similarity

1. A

2. D

3. C

4. B

5. D

6. B

7. C

8. A

1.8 Chapter 8

Quiz: Pythagorean Theorem and Geometric Mean

Name:________________________Hour:______Date:______________1. Do the following lengths yield a right triangle? 4, 14, 2

√53?

2. A rectangular parking lot measures 14mile by 5

8mile. What is the distance from one

corner to its opposite?

3. Find the geometric mean of 16 and 48.

4. Find the altitude of ABC.

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5. Do the following lengths yield an obtuse, acute, or right triangle? 12, 18, 20. Explain youranswer.

Answers: Pythagorean Theorem and Geometric Mean

1. Yes, 42 + 142 = (2√

53)2

2. .673 mile

3. 16√

3

4. 3.098

5. Acute angle 122 + 182 > 202

Quiz: Trigonometric Functions and Their Inverses

Name:________________________Hour:______Date:______________1. Using ABC, find

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a. Sin(A)

b. Cos(A)

c. AC

2. A 16’ ladder is placed along a building 5’ from its base.

a. At what angle does the ladder make with the horizon?

b. How high along the building does the ladder reach?

3. An airplane is flying at an altitude of 35, 000’ and wants to make a smooth landing ontothe runway 150 miles away. At what angle should the plane descend?

4. What happens when you type sin−1(1.1) into your calculator? Why do you think thishappens?

5. You are flying a kite with 50’ of string. The angle of elevation from the spool to the kiteis 65 degrees.

a. Draw and label a diagram to represent this situation.

b. What is the horizontal distance between you and your kite?

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Answers: Trigonometric Functions and Their Inverses

1. a. 5AC

b. 4AC

c. 6.42

2. a. 71.8

b. 15.2 feet

3. 2.5 degrees

4. Domain error; the sine values go between −1 and 1

5. 21.13’

Quiz: Acute/Obtuse Triangles

Name:________________________Hour:______Date:______________1. Your triangle has a SAS situation. Which law, the Law of Cosines or the Law of Sines,should you use? Explain your reasoning.

2. Samus wants to know how tall a tree is for his Biology project. He walks 100 feet awayfrom the base of a tree and uses an astrolabe to determine that the angle made from theground to the top of the tree is 33 degrees. The tree grows at an 85 degree angle from theground. Use this information to determine the height of the tree

3. Solve the following triangle. Draw a sketch to help you.

A =? a =?B = 65 b = 100C =? c = 89

Answers: Acute/Obtuse Triangles

1. The Law of Cosines because you have more sides than angles

2. 61.68’ tall

3. A = 62, C = 53, a = 97.42

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Chapter Test Right Triangle Trigonometry

Name:________________________Hour:______Date:______________1. A rectangular pool has dimensions 15 feet by 25 feet. How long is its diagonal?

2. An isosceles triangle has a leg length 7 cm and base length 11 cm. What is its area?

3. What is the distance between (−6,−6) and (4, 13)?

4. Do these three segments represent an acute, right, or obtuse triangle: 5, 17, 22.89?

5. How can you identify a Pythagorean Triple?

6. Find the geometric mean of 9 and 81.

7. Consider a 30 − 60 − 90 degree triangle with shortest side 7 inches. Find the lengths ofthe longer leg and hypotenuse.

8. An isosceles right triangle has hypotenuse 3√

2 kilometers. What other information canyou conclude?

9. The triangle below has an altitude a = 4√

5 cm. Find the measurements of legs m and n.

10. Using the triangle at the right:

a. Find tan(A)

b. Find measure of ∠A rounded to the nearest hundredth..

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11. The flagpole casts a 20 yard shadow. To the nearest whole yard, how tall is the flagpole?

12. Solve △ABC.

13. A 12−foot long wheelchair ramp must make a 5◦ angle with the horizon. How far awayfrom the base of the building will be the beginning of the ramp?

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Answers: Chapter Test Right Triangle Trigonometry

1. 29.15 feet

2. 23.82 cm2

3. 21.47 units

4. Acute, because 52 + 172 > 22.892

5. Sample: A Pythagorean Triple is a set of whole numbers that form a right triangle. Forexample, 3, 4, and 5 represent a Pythagorean Triple because 32 + 42 = 52.

6. 27

7. The longer leg is 7√

2 inches and the hypotenuse is 14 inches.

8. The base angles are each 45 degrees and the each leg is 3 kilometers.

9. m = 12 cm; n = 6√

5 cm

10. tan(A) = 7/12; b.∠A = 30.26 degrees11. 35 yards

12. b = 46.88, c = 39.465

13. 11.95’

Standardized Test Right Triangle Trigonometry

Name:________________________Hour:______Date:______________1. Consider a right triangle with legs j and k and hypotenuse l. Which of the following isnot true?

a. j2 + k2 = l2

b. j2 − k2 = l2

c. −j2 − k2 = −l2

d. k2 = l2 − j2

2. Which of the following is not enough information to solve a triangle?

a. Two angles

b. Two legs of a right triangle opposite angle

c. Two sides and an included angle

d. One side and the measure of its

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3. If the sum of the squares of two sides is less than the square of the longest third side,then the triangle is

a. Right

b. Acute

c. Isosceles

d. Obtuse

4. Consider a 30− 60− 90 triangle. Suppose the shortest side is 3 cm. What is the measureof the leg opposite the 60◦ angle?

a. 3 cm

b. 6 cm

c. 3√

3 cm

d. 3√

2 cm

5. Consider an isosceles right triangle. If the hypotenuse is√

72”, what is the length of thelegs?

a. 6”

b. 72”

c. 8.5”

d. 36”

6. A 30−foot ladder leans against a wall, forming a 70◦ angle with the horizon. How far upthe wall does the ladder reach?

a. 8.24’

b. 28.19’

c. 10.26’

d. 15.67’

7. Which of the following is not used to solve for a non-right triangle?

a. Sin(A)a

= Sin(C)c

b. a2 = b2 + c2

c. a2 = b2 + c2 − 2(bc ∗ cos(A))


8. Which of the following is the ratio of cosine(B)?

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a. ABBC

b. ACBC

c. BCAB

d. ACAB

Answers: Standardized Test Right Triangle Trigonometry

1. B

2. A

3. D

4. C

5. A

6. B

7. C

8. C

1.9 Chapter 9

Quiz: About Circles

Name:________________________Hour:______Date:______________1. Identify the center and radius of the circle given the following equation (x+4)2+(y)2 = 121.

2. Which of the following is a coordinate on the circle with equation (x− 2)2 +(y +3)2 = 81?

a. (0, 3)

b. (4,−1)

c. (2, 6)


3. Write the equations for three concentric circles with center (1, 0).

4. Using the circle at the right, identify:

a. Diameter

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b. Radius

c. Secant

d. Tangent

e. Chord

5. Circle A has area 484π in2. Circle B has diameter 44”. Are these circles congruent?Explain your reasoning.

Answers: About Circles

1. Center (−4, 0) with radius 11

2. C

3. Sample: (x− 1)2 + y2 = 2, (x− 1)2 + y2 = 81, (x− 1)2 + y2 = 9

4. a. CE

b.AE

c. ←→DC

d. ←→D

e. ←→BC

5. Yes, by finding the area of circle B, you can show the circles are congruent

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Quiz: Tangents to Circles

Name:________________________Hour:______Date:______________1. In the diagram, AC is a radius of circle A. Is DC tangent to the circle? Show your workto illustrate your answer.

2. True or false. The distance between the centers of two circles is equal to the length ofthe diameter of each circle.

3. DC passes through the center of circle A and FE is perpendicular to DC at point G.The radius of the circle is 5 inches and AG = 4 inches. If GF = 3 inches, what is EF?

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4. What is the perimeter of the pentagon pictured below?

Answers: Tangents to Circles

1. No, by the converse of Pythagorean’s Theorem, 1.52 + 2.672 ̸= 2.952. Therefore, angle Cis not right and DC is not tangent to the circle

2. True

3. 6 inches

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4. 19.6 cm

Quiz: Arc Measures, Chords, and Inscribed AnglesName:________________________Hour:______Date:______________1. Minor arc XZ has measurement 99 degrees. What is the measurement of major arcXY Z?

2. Suppose⊙

R is congruent to⊙

M . Given that arc AB is congruent to arc CD, whatcan you conclude? (Draw a picture of the situation to help illustrate your solution)

3. Two concentric circles have radii 6 m and 12 m. A segment tangent to the smaller circleis a chord of the larger circle. What is the length of the segment?

4. A 22” chord is 10” from the center of a circle. What is the radius of the circle?

5. The measure of arc BC is 125 degrees, which is intercepted by the inscribed angle ∠BDC.What is the measure of the angle?

Answers: Arc Measures, Chords, and Inscribed Angles1. 261

2. You can conclude that central angles ∠ARB and ∠CMD are congruent3. 10.39”

4. 14.866”

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5. 62.5

Quiz: Angles and Segments of Chords, Secants, and Tan-gents

Name:________________________Hour:______Date:______________Find the measure of each unknown.

1. Given: Diagram at the right, EC = 12, and BC = 26; determine: m∠CED and ED.

2. Given: Diagram at the right, DF = 6, FE = 12, FB = 10. Find m∠1 and x.

3. Given: Diagram at the right. Find m and m∠BFD.

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4. Explain the difference between a tangent segment and a secant segment.

Answers: Angles and Segments of Chords, Secants, and Tan-gents

1. ∠BED = 39, ED = 21.352. m∠1 = 51, x = 7.23. m∠BFD = 42,m = 4.54. A tangent segment touches a circle at one point while a secant segment intersects a circlein two points.

Chapter Test Circles

Name:________________________Hour:______Date:______________1. Using the circle below, label an example of the following:

a. Chord:

b. Secant:

c. Tangent:

d. Diameter:

e. Radius:

f. Central Angle:

g. Major arc:

h. Minor arc:

i. Semicircle:

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2. What is the equation for the circle at the right?

3. What is the diameter and center of the circle with equation (x + 4)2 + (y − 7)2 = 10 ?

4. Draw a vertical tangent to the circle below.

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5. Find the missing segments using the diagram below.

6. Find the distance between the centers of circles A and B.

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7. Determine the measures of as many arcs as you can. You can assume PL and QM arediameters of circle O.

Answers: Chapter Test Circles

a. Chord: Sample: HG

b. Secant: Sample: ←→HG - the extension of chord HG

c. Tangent: ←→DE

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d. Diameter: AC

e. Radius: Sample - BC

f. Central Angle: Sample - ∠GBCg. Major arc: Sample - arc AGH

h. Minor arc: Sample – arc ADH

i. Semicircle: arc ADC

2. (x + 4)2 + (y − 1)2 = 4

3. Center = (−4, 7) with diameter 2√

10 units

4. Sample below

5. EB = 3 units, AD = 12 units, BF = 9 units, EF = 12 units, ED = 15 units, DF =21 units

6. 5.60 units

7. Arcs: PO = 60, OL = 120, PM = 120, PML = 180, POL = 180

Standardized Test CirclesName:________________________Hour:______Date:______________1. A segment whose endpoints lie on the boundary of a circle is called a(n)

a. Tangent

b. Secant

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c. Chord

d. Diameter

2. In congruent circles, chords are congruent if

a. They have congruent arcs

b. They are parallel

c. They are proportional


3. A circle has equation (x− 2)2 + (y + 7)2 = 36. What is its center?

a. (2, 7)

b. (0, 0)

c, (6, 6)

d. (2,−7)

4. A 14 cm chord is 6 cm from the center. What is the radius of the circle?

a. 9.21 cm

b. 3.61 cm

c. 6 cm

d. 85 cm

5. The diameter of a circle is 20 inches and a chord of the circle is 12 inches. How far is thechord from the center of the circle?

a. 64 inches

b. 8 inches

c. 11.66 inches

d. 136 inches

6. A circle has center (11, 1) and radius√

10. What is its equation?

a. (x + 11)2 + (y + 1)2 = 10

b. (x + 11)2 + (y − 1)2 = 10

c. (x− 11)2 + (y + 1)2 = 10

d. (x− 11)2 + (y − 1)2 = 10

7. In which case is the measure of an angle half of the sum of the intercepted arcs?

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a. Angles outside the circle

b. Angles on the circle

c. Angles inside the circle


8. The measure of arc AB = 167◦. What is the measure of its inscribed angle?

a. 83.5

b. 167

c. Cannot be determined


9. How many tangents do these circle share?

a. 0

b. 1

c. 3

d. 2

Answers: Standardized Test Circles

1. C

2. A

3. D

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4. A

5. B

6. D

7. C

8. A

9. D

1.10 Chapter 10

Quiz: Areas of Triangles, Quadrilaterals, and Similar Poly-gons

Name:________________________Hour:______Date:______________1. The area of a triangle is 75 un2 and base length 15 units. What is the length of itsaltitude?

2. Find the area of the trapezoid below.

3. Two pentagons have a ratio of similarity of 56. The area of the smaller pentagon is 212 ft2.

What is the area of the larger figure?

4. Compare and contrast the area formulas for parallelogram, kite, trapezoid, and rhombus.How do each of these relate to the area of a triangle?

5. Why does it make sense that the units of area are expressed using the squared exponent?

6. Sketch the figure and determine its perimeter and area. The figure is a rhombus. Its sidelength is 7 units and the length of one of its diagonals is 15 units.

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Answers: Areas of Triangles, Quadrilaterals, and SimilarPolygons

1. 10 units

2. 9.75 un2

3. 305.28 ft2

4. With the exception of the rhombus, all formulas involve the altitude and a base. Paral-lelograms are two triangles sharing their longest side.

5. Area involves the multiplication of two values. Each value has a unit. So unit∗unit = unit2

6. Perimeter = 28 units, area = 43.27 units

Quiz: Circumference, Arc Length, Area of Circles, and Areaof Sectors

Name:________________________Hour:______Date:______________1. A pepperoni pizza has 14” diameter.

a. What is its circumference?

b. What is its area?

c. Suppose the pizza is cut into 8 slices.

i. What is the arc length of one slice?

ii. What is the area of 3 slices?

2. A monster truck tire is 42 inches in diameter. How many revolutions does the tire makewhile traveling one mile?

3. The arc length of 120 degrees of a cinnamon roll is 6.28 inches. What is the radius of theroll?

4. A circle is inscribed in a square. The square has a side length of 10 mm. What is thearea of the circle?

5. What is the area of a 57 degree sector of a circle with diameter 3 units? �

Answers: Circumference, Arc Length, Area of Circles, andArea of Sectors

1. a. 14π ≈ 43.98 inches

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b. 49π ≈ 153.99 in2

c. i. 5.50 inches

ii. 51.33 in2

2. 480.18 revolutions

3. Approximately 3 inches

4. 25π ≈ 78.53 mm2

5. 1.12 un2

Quiz: Areas of Regular Polygons and Geometric Probability

Name:________________________Hour:______Date:______________1. A regular heptagon has side length 42 cm and apothem 36 cm. Determine its area.

2. Find the area of a regular hexagon with radius 10 feet.

3. Define geometric probability.

4. Suppose school starts at 8:00 and ends at 4:00. You eat lunch at 12:00 p.m. If there is afire drill at a random time during the day, what is the probability it will happen after lunch?

5. A regular nonagon has side length 6 units and area of 788 un2. What is the length of theapothem?

6. Draw a sketch of the following situation and answer the question. Circles A and B areconcentric. Circle A has a radius 2.5 cm; circle B has diameter 30 cm. If you threw a dart,what is the probability you will land in circle A?

Answers: Areas of Regular Polygons and Geometric Proba-bility

1. 5, 292 cm2

2. 259.81 ft2

3. Probability that involves geometrical figures and/or quantities such as area or length

4. 12or 50%

5. 29.19 un

6. 2.78%

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Chapter Test Perimeter and Area

Name:________________________Hour:______Date:______________1. The length of a rectangle is 15 more than its width and encompasses an area of 356 in2.What is a possibility for the rectangle’s dimensions?

2. Find the area of the triangle below.

3. An isosceles trapezoidal table is sketched below. Find its area in square inches. (2.54 cm =1 inch).

4. The area of a square is 196 mm2. Determine its perimeter in centimeters.

5. The distance between Milwaukee, Minnesota and Phoenix, Arizona is 8.5” on a map. Thescale is 1 inch = 200 miles. What is the true distance between these two cities?

6. Two parallelograms have a ratio of perimeters of 56. Suppose the perimeter of the smaller

parallelogram is 34 feet. What is the perimeter of the larger parallelogram?

7. A 16” diameter pizza has

a. _________________ circumference and ________________ area.

b. Suppose that pizza is cut into 10 slices. Determine:

i. The arc length of 3 slices of pizza.

ii. The area of 2 slices of pizza.

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8. The perimeter of a regular nonagon is 81y units. What is the length of a side?

9. An octagon with side length 5” has an apothem of 4.25”. Determine its area.

10. The distance between Acton and Barton is 30 miles, between Barton and Dayton is95 miles, and between Canton and Dayton is 24 miles. What is the probability your car willhave a flat between Barton and Canton?

11. A rhombus has an area of 64 m2. What is the product of its diagonals?

12. How many degrees does a minute hand of a clock travel from 12:00 to 4:00?

13. Suppose the length of the minute hand of a clock is 8 inches. How far would the minutehand travel from 12:00 to 4:00?

Answers: Chapter Test Perimeter and Area

1. 12.804” wide and 27.804” long

2. 7.5 square units

3. 250.43 square inches

4. 56 mm

5. 1, 700 miles

6. 40.8 feet

7. a. 16π ≈ 50.265 inches, 64π ≈ 201.06 square inches

b. i. 15.0795 inches

ii. 40.21 square inches

8. 9y units

9. 85 square inches

10. 56.8%

11. 128 m

12. 1, 440 degrees

13. 201.06 inches

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Standardized Test Perimeter and Area

Name:________________________Hour:______Date:______________1. What is the area of a regular pentagon whose apothem is 35.6 cm and side length is47 cm?

a. 1673.20 cm2

b. 82.6 cm2

c. 8366 cm2

d. 4183 cm2

2. Which statement is false?

a. The height of the parallelogram is always inside the figure

b. Either pair of parallel sides can be used as the “base.”

c. If two parallelograms are congruent, then they have the same area.

d. If you translate a parallelogram in the coordinate plane, the area remains the same.

3. What is the length of the base of a triangle with altitude 9 cm and area 618 cm2?

a. 34.33 cm

b. 137.33 cm

c. 68.67 cm


4. What is the probability that you look at a clock and the second hand is between the 4and 6?

a. 23

b. 13

c. 12

d. 16

5. Which is not true about probability?

a. It can be expressed as a fraction, percent, or decimal

b. It is a ratio of the wanted outcome to the entire possibilities]

c. It can be greater than 1

d. To express the probability of event B, you can write P (B)

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6. An orange has 3” diameter. What is its circumference?

a. 4.71 inches

b. 9.42 inches

c. 7.07 inches

d. 28.27 inches

7. An angle measures 100 degrees. What fraction is this of the circle?

a. 518

b. 13

c. 14

d. 58

8. What is the radius of a ball that rolls 210 feet in 50 revolutions?

a. 4.2 feet

b. 0.24 feet

c. 1.34 feet

d. 0.67 feet

1.11 Chapter 11

Quiz: Polyhedron and Representing Solids

Name:________________________Hour:______Date:______________1. Define polyhedron.

2. Consider a pentagonal prism. Write the number of:

a. Faces:

b. Vertices:

c. Edges:

3. Use Euler’s Formula to determine the number of vertices regular dodecahedron.

4. Draw the orthographic view of the image below.

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commons.wikimedia.org/wiki/File:Birdhouse_030.jpg

Answers: Polyhedron and Representing Solids

1. A closed plane figure formed by three or more segments such that each intersects twosides at their endpoints; a three dimensional figure made up of polygons.

2. a. 7

b. 10

c. 15

3. 30

4. Answers may vary

Quiz: Surface Area and Volume of 3-dimensional Figures

Name:________________________Hour:______Date:______________1. A pencil holder is shaped like the figure below, with a 3” diameter and height of 4 inches.How much metal would it take to make the sides and bottom, leaving the top open?

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2. How much cardboard does it take to make a cereal box 11.5” tall, 8.5” wide, and 3.5”deep? How much cereal could it hold?

3. The Pyramid of Kafre is a right square pyramid is 144 meters tall with a base side lengthof 215 meters. Determine its volume.

4. Sketch the solid and determine its surface area and volume. A right cone with diameterof 18 cm and a slant height 25 cm.

5. What is the relationship between a prism and a pyramid with identical base and height?

Answers: Surface Area and Volume of 3-dimensional Figures

1. 44.77 in2

2. 335.5 square inches of cardboard to make; holds 342.13 in2

3. 2, 218, 800 m3

4. SA = 706.86 cm2, V = 1978.92 cm3

5. The volume of a pyramid is one-third the volume of its corresponding prism

Quiz: Spheres and Similar Solids

Name:________________________Hour:______Date:______________1. A yarn ball has diameter 4 inches. What is its volume?

2. How much material is needed to build a hollow globe with diameter 20 inches?

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3. The volume of a sphere is 288 cm3. What is its diameter?

4. A hemispherical hanging planter has a radius of 7 inches. How much dirt can it hold?

5. Two similar prisms have heights 8 mm and 20 mm.

a. What is the ratio of similitude?

b. What is the ratio of their volumes?

c. How do their surface areas compare?

6. Rectangle prism A has dimensions l, w, and h. Rectangular prism B is twice as long andtwice as wide. How do their volumes compare?

Answers: Spheres and Similar Solids

1. 33.52 in3

2. 1256.64 in2

3. 8.19 cm

4. 718.38 in3

5. a. 2.5

b. 15.625

c. 6.25

6. The volume of prism B is 4 times that of prism A

Chapter Test Surface Area and VolumeName:________________________Hour:______Date:______________1. a. Name the figure below. Be as specific as possible!

b. List the values of the following:

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i. Edges:

ii. Faces:

iii. Lateral faces:

iv. Bases:

v. Lateral edges:

2. What is true about a polyhedron? How do polyhedra differ from prisms?

3. Draw the orthographic view of the doghouse illustrated below.

www.freeclipartnow.com/.../Doghouse.jpg.html

4. Draw the net of a truncated right pentagonal pyramid.

5. Find the surface area of the right hexagonal prism below.

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6. The barn below is to be painted with two coats of paint on all sides. If one gallon of paintcovers 150 ft2, how many gallons of paint must you buy?

7. Draw a net of the below cylinder (does not have to be drawn to scale). What is its surfacearea and volume of the cylinder?

8. How do the volumes of the two figures below compare?

9. According to Cavelieri’s Principle, two figures will have the same volume if ____________.

10. Find the surface area and volume of the pyramid below. Assume the length of the baseis 11 mm and its sla

geometry teacher’s edition - assessment - ck-12...

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