ANSWERS

STUDY GUIDE FOR THE FINAL EXAM

CHAPTER 1

Use the diagram to answer the following questions #1-3.

1. Give two other names for . Sample answer: PN

2. Give two other names for plane . Sample answer plane SAN

3. Name three points that are collinear. Name four points that are coplanar.

Sample answer: NWP

4. Classify the polygon by the number of sides. Tell whether it is convex or concave.

Octagon

Convex

5. Write three names for the angle.

Y, LYT, TYL

In the figure, , , , and .

6. Name a pair of complementary angles. PSO, RQD

7. Name a pair of supplementary angles. ZQR, TSO

8. Name a pair of adjacent angles. ZQR, RQD

PSO, TSO

9.Point M is the midpoint of . Find BM.

29

10. You are making a picture frame in shop class. Two pieces of wood are cut to form complementary

angles so they fit together properly. One angle needs to be and the other angle needs to be

. What is the measure of the larger angle? 51

A BM

4x + 13 3x + 17

S

P

O

T

Q

Z

QQR

D

W

aF

d

P

NA

DO

S

Y

T

L

11.Two angles form a linear pair. The measure of one angle is eight times the measure of the other angle. Find

the measure of the larger angle. 160

12.The measure of an angle is nine times the measure of its complement. Find the measure of the larger angle.

81

13.Point B is between points A and D, and point C is between points B and D. Which are possible lengths of

when , , and ?

65 <x < 82

14. The midpoint of is . One endpoint is . Find the coordinates of endpoint G.

(-8, -10)

15. Find the area of the polygon with vertices , , , and .

28

16. Find the perimeter of the polygon with vertices , , , and .

30.44

17. In the diagram, . Find .

82

18. The midpoint of segment JK is M(6, 3).

One endpoint is J (14,9).

Find the coordinates of endpoint K.

(-2,-3)

Chapter 2

19. Find the values of x and y. x= 8 y= 14

20. In the diagram, and . Which angle measures are possible?

26 and 64

(5x + 2)°

(5y + 68)°

(3x + 18)°

(3y + 96)°

1

2

3

4

5

D A

B

C

(7x + 34)°

(9x + 46)°

In the diagram, AB = CD, BC = 3, AC = , and BD = . Match the numbered equation

or reason below with its corresponding letter (a - g) to show that AB = .

Equation Reason

1. , ,

,

1. Given

2. 2.

3. 3.

4. 4. Segment Addition Postulate

5. 5.

6. 6.

7. 7. Addition

8. 8. Addition

9. 9.

10. 10.

11. 11. Simplify

12. 12.

a. e. b. f.

c. g.

d. Segment Addition Postulate

___E_21. Equation 2

___D_22. Reason 3

___F_23. Reason 5

___A_24. Equation 6

__B__25. Reason 9

___G_26. Equation 10

___False_ 27. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the conditional

statement. Then decide whether it is true or false. If an animal is a dog, then the animal is a golden

retriever.

__True__ 28. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the converse.

Then decide whether it is true or false. If an animal is a golden retriever, then the animal is a dog.

A

E

B C D3

__True__ 29. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the inverse.

Then decide whether it is true or false. If an animal is not a dog, then the animal is not a golden retriever.

____False 30. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the

contrapositive. Then decide whether it is true or false. If an animal is not a golden retriever, then the

animal is not a dog.

___A_31. If and , then .

a. Transitive Property of Angle Congruence

b. Symmetric Property of Angle Congruence

c. Reflexive Property of Angle Congruence

State the postulate illustrated by the diagram.

___B_32.

a. Plane Intersection Postulate c. Two Point Postulate

b. Plane-Line Postulate d. Line-Point Postulate

__C__33.

a. Two-Point Postulate c. Three Point Postulate

b. Plane-Point Postulate d. Plane Intersection Postulate

__D__34.

a. Two Point Postulate c. Three Point Postulate

b. Line Intersection Postulate d. Line-Point Postulate

___A_35.

a. Plane Intersection Postulate c. Plane-Point Postulate

b. Plane-Line Postulate d. Line Intersection Postulate

___D_36.

a. Two Point Postulate c. Line-Point Postulate

b. Plane-Line Postulate d. Line Intersection Postulate

Identify the numbered statement or reason in the two-column proof.

Given

Prove

STATEMENTS REASONS

1.

1. Given

2. 2.

3.

3.

4. 4. Transitive Property of Equality

5. 5.

6. 6. Subtraction Property of Equality

___B_37. What is Reason 2?

a. Subtraction Property of Equality c. Reflexive Property of Equality

b. Transitive Property of Equality d. Symmetric Property of Equality

__C__38. What is Reason 3?

a. Definition of complementary angles c. Angle Addition Postulate

b. Substitution Property of Equality d. Linear Pair Postulate

_A___39. What is Statement 4?

a. b. c. d.

__D__40. What is Reason 5?

a. Addition Property of Equality c. Multiplication Property of Equality

b. Angle Addition Postulate d. Substitution Property of Equality

CHAPTER 3

41. In th36e diagram, . Find the value of y.

36

SKIP THIS QUESTION 42.Find the value of x that makes .

50 43. Write an equation of the line passing through the point that is parallel to the line .

y= 2/3 x – 10/3

44. Write an equation of the line passing through the point (9, 3) that is perpendicular to the line .

y= 17/7 x – 132/7

In the diagram, think of each segment in the figure as part of a line.

b

c

74°

+ 34)°y(2

a b

c

d55°

(2x + 25)°

45. Name the line(s) through point D that appear parallel to .

a.

c. and

b.

d.

46. Name the line(s) through point B that appear skew to .

a.

c.

b. and

d. and

47. Name the line through point D that appears perpendicular to .

a.

c.

b.

d.

48. Classify the pair of numbered angles.

Alternate Interior Angles

49. Classify the pair of numbered angles.

Consecutive Interior Angles

50. Classify the pair of numbered angles.

Corresponding Angles

List all:

51. Corresponding angles: 3-5, 2-4, 6-8, 1-7

52. Alternate Interior angles: 3-7, 4-8

53. Alternate Exterior angles: 2-6, 1-5

54. Consecutive Interior angles: 7-8, 3-4

55. Find the value of x.

16

56. Find the value of x that makes line s parallel to line t.

18

57. Find the distance from point P to .QS

4.47

58. Write an equation of the line passing through point 1, 4P that is parallel

to 6 8.y x y= - 6x -10

59. Write an equation of the line passing through point 1, 3P that is

perpendicular to 4 7.y x y= -1/4 x + 11/4

CHAPTER 4

60. Graph with endpoints C(–8, 2) and D(–5, 6) and its image after the composition.

Translation:

Translation:

61. The logo for a business is moved across a page 6 units right and 6 units down. Next, it is moved 2 units

left and 2 units up. Rewrite the composition as a single translation.

(x+4, y-4)

(–8, 2)

(–5, 6)

C

D

(–5, 1)

(–2, 5)D'

C'

–2–4–6–8 x

2

4

6

8

y

62. Graph with points F(–3, –4) and G(–3, –2)

and its image after the reflection in the line .

Image of F (4,3) and image of G (2,3)

63. Describe the similarity transformation that maps to (dilations have a center at the

origin).

A

B

C

R

S

T

4 8 12–4–8–12 x

4

8

12

–4

–8

–12

y

a. rotation 180° about the origin followed by a dilation with a

scale factor of

b. rotation 90° counterclockwise about the origin followed by a

dilation with a scale factor of

c. rotation 180° about the origin followed by a dilation with a

scale factor of

64. You are rotating a figure 152° from G to . Find the measure of the acute angle formed by

intersecting lines so that G can be mapped to using two reflections. 76

65. Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.

66. Graph with endpoints at and

and its image after the composition.

Translation:

Rotation: 90° counterclockwise about the origin

C

P

P'

12

CP = 42

d. rotation 90° counterclockwise about the origin followed by a

dilation with a scale factor of

a. 30; enlargement c. 30; reduction

b. ; reduction

d. ; enlargement

2

7

7

2

67. In the diagram, , is reflected in line k, is reflected in line j, centimeters, and the

distance from to line j is 12 centimeters. Which of the following statements are true?

68. Graph with endpoints at and

and its image after the composition.

Rotation: 180° about the origin

Reflection: in the line

S

T

S''

T''

2 4–2–4 x

2

4

–2

–4

y

B

A

k

A'

B'

j

B''

A''

a. The distance from A to line k is 3

centimeters.

b. cm

c. line j

d. A rotation maps onto .

ABC

69. How many lines of symmetry does the rhombus have? 2

Chapter 5

70. A ramp is designed with the profile of a right triangle. The measure of one acute angle is 2 times the

measure of the other acute angle. Find the measure of each acute angle. 30 60

71. Find . 112

S

T

S'

T'

S''

T''

2 4–2–4 x

2

4

–2

–4

y

72. Find the value of x. 13

Can the triangles be proven congruent with the information given in the diagram? If so, state the

theorem you would use.

73.

Yes

AAS

40°

28°

A

BC60° 60°

13

x

74.

No

75. Which reason is not necessary to explain how you can find the distance across the lake?

a. ASA Congruence Theorem

b. Right Angles Congruence Theorem

c. SSS Congruence Theorem

d. Corresponding parts of congruent triangles are congruent.

e. Vertical Angles Congruence Theorem

76. Which reason is not used in a plan to prove that ?

a. ASA Congruence Theorem c. SSS Congruence Theorem

b. Reflexive Property of Congruence d. Congruent Complements Theorem

77. Which reason is not used in a plan to prove that ?

a. HL Congruence Theorem c. Base Angles Theorem

b. Reflexive Property of Congruence d. Corresponding parts of congruent triangles

are congruent.

78. Which reason is not used in a plan to prove that ?

a. Corresponding parts of congruent triangles

are congruent. c. Congruent Complements Theorem

b. Reflexive Property of Congruence d. Alternate Interior Angles Theorem

SKIP THIS QUESTION 79. In the diagram, passes through the center C of the circle and

. Name two triangles that are congruent.

a. c. b. d. not enough information

Match the numbered statement below with its reason to prove that .

a. Third Angles Theorem

b. Given

c. All corresponding parts are congruent.

d. Reflexive Property of Congruence

__B__80. 1.

__B__81. 2.

__A__82. 3.

__B__83. 4.

___D_84. 5.

__B__85. 6.

__C__86. 7.

CHAPTER 6

In Exercises 87-90, find the indicated measure. Explain your reasoning.

87. AD 20 88. GJ 17

89. PQ 14 90. m DGF 76

In Exercise 91, find the coordinates of the circumcenter of the triangle with the

given vertices.

91. 6, 0 , 0, 0 , 0, 4J K L

(3,2)

In Exercise 92, P is the incenter of triangle QRS. Use the given information to

find the indicated measure.

92. 4 8,PJ x 7PL x

Find .PK 12

In Exercises 93-94, point P is the centroid of triangle ABC. Use the given

information to find the indicated measures.

93. 12BL 94. 16CP

Find BP 8 and PL 4 Find PL 8 and CL 24

In Exercise 95, find the coordinates of the centroid of the triangle with the given

vertices.

95. 2, 6 , 4, 0 , 10, 6Q R S (4,4)

In Exercises 96-100, use the graph of triangle ABC.

96. In triangle ABC. show that the midsegment ED

is parallel to BC and that 12

.ED BC

The slope of 1 4

3,2 1

ED

and the slope of 2 4

3.5 3

BC

So, || .ED BC

2 2

2 1 1 4 10,ED 2 2

5 3 2 4 2 10,BC so 1

.2

ED BC

97.Find the coordinates of the endpoints of

midsegment ,EF which is opposite .AC

1, 4 , 4,1E F

98. Show that EF is parallel to AC and that 12

.EF AC

The slope of 1 4

1,4 1

EF

and the slope of

2 41.

5 1AC

So, || .EF AC

2 2

4 1 1 4 3 2,EF 2 2

5 1 2 4 6 2,AC so 1

.2

EF AC

99. State the coordinates of the endpoints of midsegment .DF

2,1 , 4,1D F

100. Show that DF is parallel to AB and 12

.DF AB

The slope of 1 1

0,4 2

DF

and the slope of

4 40.

3 1AB

So, || .DF AB 4 2 2,DF and

3 1 4,AB so 1

.2

DF AB

In Exercises 101-103, use triangle QRS, where A, B, and C are the midpoints of

the sides.

101. When 16,AB what is QS? 32

102. When 3 1 and 5 4,CA x SR x what is CA?17

103. When 5 2 and 2 5,QR x CB x what is AR? 21

In Exercises 104-105, list the angles of the given triangle from smallest to

largest.

104. 105.

N,L,M F=D, E

In Exercises 106-107, list the sides of the given triangle from shortest to longest.

106. 107.

AB, AC, BC QP,PR,QR

In Exercises 108-109, is it possible to construct a triangle with the given side

lengths? Explain.

108. 15, 37, 53 No 109. 9, 16, 8 Yes

In Exercises 110-113, copy and complete the statement with , , or . Explain your reasoning.

110. AC > 𝐷𝐹 111. HGI = IGJ

112. 1< 2 113. KL< 𝑴𝑵