Review for Final - Geometry A

Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 1. Based on the pattern, what are the next two terms of the sequence?

5, 14, 23, 32, . . . a. 41, 50 b. 288, 2592 c. 50, 59 d. 41, 2592

____ 2. Alfred is practicing typing. The first time he tested himself, he could type 35 words per minute. After

practicing for a week, he could type 38 words per minute. After two weeks he could type 41 words per minute. Based on this pattern, predict how fast Alfred will be able to type after 4 weeks of practice. a. 47 words per minute c. 51 words per minute b. 44 words per minute d. 41 words per minute

____ 3. Name the plane represented by the top of the box.

a. ACD b. ACF c. BCG d. AEI

____ 4. Are points G, K, and F collinear or noncollinear?

a. collinear b. noncollinear c. impossible to tell

____ 5. Name the intersection of plane RNP and plane MNP.

a. c. b. d. The planes need not intersect.

____ 6. Name a fourth point in plane YZT.

a. S b. T c. Z d. U

____ 7. Name the ray in the figure.

M N

a. b. c. d.

____ 8. Which plane is parallel to plane ABFE?

a. plane BDHF b. plane ACGE c. plane CDHG d. plane EFHG

____ 9. Find AD.

0 1 2 3 4 5 6 7 8 9 100–1–2–3–4–5–6–7–8–9–10

A B C D

a. 8 b. 1 c. 15 d. 17

____ 10. If find the values of x, EF, and FG. The drawing is not to scale.

E GF

a. x = 11, EF = 8, FG = 13 c. x = 6, EF = 8, FG = 13 b. x = 6, EF = 40, FG = 23 d. x = 11, EF = 28, FG = 28

____ 11. If T is the midpoint of find the values of x and ST. The diagram is not to scale.

S UT

6x 4x + 20

a. x = 15, ST = 77 c. x = 10, ST = 77 b. x = 15, ST = 60 d. x = 10, ST = 60

____ 12. If and , then what is the measure of The diagram is not to scale.

a. 55 b. 64 c. 9 d. 46

____ 13. If and then what is the measure of The diagram is not to scale.

a. 40 b. 39 c. 78 d. 79

____ 14. If then what are and The diagram is not to scale.

a. , c. , b. , d. ,

____ 15. The complement of an angle is 62°. What is the measure of the angle?

a. 28° b. 38° c. 118° d. 128°

____ 16. and are supplementary angles. , and . Find the measure of each angle.

a. c. b. d.

____ 17. bisects and Solve for x and find The

diagram is not to scale.

a. x = 15, c. x = 15, b. x = 14, d. x = 14,

____ 18. Find the distance between points P(2, 1) and Q(9, 6) to the nearest tenth.

a. 8.6 b. 13 c. 74 d. 12

____ 19. Find the coordinates of the midpoint of the segment whose endpoints are H(8, 5) and K(6, 9).

a. (7, 7) b. (1, 2) c. (14, 14) d. (2, 4)

____ 20. Find the midpoint of

a. (–2, –2) b. (–1, –1) c. (–1, –2) d. (–2, –1)

____ 21. Find the circumference of the circle in terms of π.

35 in.

a. 1225π in. b. 35π in. c. 70π in. d. 140π in.

____ 22. Find the circumference of the circle to the nearest tenth.Use 3.14 for π.

24 m

a. 1808.6 m b. 301.4 m c. 75.4 m d. 150.7 m

____ 23. Find the area of a rectangle with base 43 cm and height 5 m.

a. 215 cm b. 215 m c. 21,500 m d. 21,500 cm

____ 24. Find the area of the circle in terms of π.

24 in.

a. 576π in.2 b. 24π in.2 c. 48π in.2 d. 144π in.2

____ 25. The figure is formed from rectangles. Find the total area. The diagram is not to scale.

7 ft3 ft

3 ft

10 ft

a. 70 b. 34 c. 58 d. 109

____ 26. Identify the hypothesis and conclusion of this conditional statement:

If two lines intersect at right angles, then the two lines are perpendicular. a. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are

perpendicular. b. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are not

perpendicular. c. Hypothesis: The two lines are not perpendicular. Conclusion: Two lines intersect at right

angles. d. Hypothesis: The two lines are perpendicular. Conclusion: Two lines intersect at right

angles.

____ 27. What is the conclusion of the following conditional?

A number is divisible by 5 if the number ends with digits 0 or 5. a. If a number ends with the digit 0 or 5, then the number is divisible by 5. b. The number ends with digits 0 or 5. c. The number is odd. d. The number is divisible by 5.

____ 28. What is the converse of the following conditional?

If a point is in the fourth quadrant, then its coordinates are negative. a. If the coordinates of a point are negative, then the point is in the fourth quadrant. b. If a point is not in the fourth quadrant, then the coordinates of the point are not negative. c. If a point is in the fourth quadrant, then its coordinates are negative. d. If the coordinates of a point are not negative, then the point is not in the fourth quadrant.

____ 29. Use the Law of Detachment to draw a conclusion from the two given statements.

If two angles are supplementary, then the sum of their measures is 180°.

and are supplementary. a. is congruent to . c. + = 90 b. + = 180 d.

____ 30. Use the Law of Syllogism to draw a conclusion from the two given statements.

If a number is a multiple of 64,then it is a multiple of 8. If a number is a multiple of 8, then it is a multiple of 2. a. The number is a multiple of 8.

b. If a number is a multiple of 64, then it is a multiple of 2. c. The number is a multiple of 2. d. If a number is not a multiple of 2, then the number is not a multiple of 64.

Fill in each missing reason.

____ 31. Given: , , and .

Find x.

Q

P

QQ SQ

R

Drawing not to scale

a. _____ x – 9 + x + 5 = 100 b. Substitution Property

2x – 4 = 100 c. Simplify 2x = 104 d. _____

x = 52 e. Division Property of Equality a. Protractor Postulate; Addition Property of Equality b. Protractor Postulate; Subtraction Property of Equality c. Angle Addition Postulate; Addition Property of Equality d. Angle Addition Postulate; Subtraction Property of Equality

____ 32. Given:

Prove:

a. a. Given b. Substitution Property c. Subtraction Property of Equality d. Division Property of Equality e. Symmetric Property of Equality

c. a. Given b. Substitution Property c. Subtraction Property of Equality d. Division Property of Equality e. Reflexive Property of Equality

b. a. Given d. a. Given

b. Symmetric Property of Equality c. Subtraction Property of Equality d. Division Property of Equality e. Reflexive Property of Equality

b. Substitution Property c. Subtraction Property of Equality d. Addition Property of Equality e. Symmetric Property of Equality

____ 33. Name the Property of Equality that justifies the statement:

If g = h, then . a. Reflexive Property c. Transitive Property b. Addition Property d. Multiplication Property

____ 34. Which statement is an example of the Symmetric Property of Equality?

a. If p = q then c. If k = p then . b. If p = q then d. k = p

____ 35. Name the Property of Congruence that justifies the statement:

If . a. Symmetric Property c. Reflexive Property b. Transitive Property d. none of these

____ 36. Name the Property of Congruence that justifies the statement:

If . a. Transitive Property c. Reflexive Property b. Symmetric Property d. none of these

Use the given property to complete the statement.

____ 37. Transitive Property of Congruence

If ______. a. c. b. d.

____ 38. Substitution Property of Equality

If , then ______. a. c. b. d.

____ 39. Find the value of x.

(6x – 4)°

(5x + 12)°

Drawing not to scale

a. 92 b. 16 c. 88 d. –16

____ 40. Find

12

34

Drawing not to scale

a. 28 b. 162 c. 152 d. 18

____ 41. Find the values of x and y.

a. x = 21, y = 61 c. x = 63, y = 117 b. x = 61, y = 21 d. x = 117, y = 63

____ 42. Line r is parallel to line t. Find m 5. The diagram is not to scale.

r

t

71 3

265

4

145°

a. 135 b. 25 c. 145 d. 35

This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways.

____ 43. If ∠8 measures 106, what is the sum of the measures of ∠1 and ∠4?

a. 286 b. 106 c. 148 d. 212

____ 44. How are and related?

a. corresponding angles c. same-side interior angles b. alternate interior angles d. none of these

____ 45. . Find the value of x for p to be parallel to q. The diagram is not to scale.

p q

1 23 4

5 6

a. 126 b. 123 c. 129 d. 42

____ 46. Find the value of k. The diagram is not to scale.

56°

46° k °

a. 124 b. 102 c. 10 d. 78

____ 47. Find the values of x, y, and z. The diagram is not to scale.

35°

62°

12°

x° y°z°

a. c. b. d.

____ 48. Classify the triangle by its sides. The diagram is not to scale.

9

95

a. scalene b. isosceles c. equilateral d. straight

____ 49. Classify ABC by its angles, when m A = 20, m B = 89, and m C = 71.

a. straight b. acute c. obtuse d. right

____ 50. Find the value of x. The diagram is not to scale.

138°

71°

x°

a. 67 b. 42 c. 161 d. 113

____ 51. Classify the polygon by its sides.

a. triangle b. octagon c. hexagon d. pentagon

____ 52. Find the sum of the measures of the angles of the figure.

a. 1440 b. 900 c. 1080 d. 720

____ 53. How many sides does a regular polygon have if each exterior angle measures 30?

a. 15 sides b. 12 sides c. 11 sides d. 14 sides

____ 54. The sum of the measures of two exterior angles of a triangle is 252. What is the measure of the third exterior

angle? a. 108 b. 72 c. 118 d. 98

____ 55. If BCDE is congruent to OPQR, then is congruent to

a. b. c. d.

____ 56. Use the information given in the diagram. Tell why and

a. Given, Reflexive Property b. Reflexive Property, Transitive Property c. Transitive Property, Reflexive Property d. Given, Given

____ 57. The two triangles are congruent as suggested by their appearance. Find the value of b. The diagrams are not to

scale.

d°

e°f°

b

c

g

3

45

44°

46°

a. 46 b. 4 c. 3 d. 5

____ 58. Justify the last two steps of the proof.

Given: and Prove:

R

S T

U Proof: 1. 1. Given 2. 2. Given 3. 3. 4. 4.

a. Symmetric Property of ; SSS c. Reflexive Property of ; SAS b. Reflexive Property of ; SSS d. Symmetric Property of ; SAS

____ 59. Name the angle included by the sides and

N

P

M

a. b. c. d. none of these

____ 60. What is the missing reason in the two-column proof?

Given: bisects and bisects Prove:

A

D

C

B

><

Statements Reasons

1. bisects 1. Given 2. 2. Definition of angle bisector 3. 3. Reflexive property

4. bisects 4. Given 5. 5. Definition of angle bisector 6. 6. ? a. AAS Theorem c. SAS Postulate b. SSS Postulate d. ASA Postulate

____ 61. Supply the missing reasons to complete the proof.

Given: and

Prove:

I

LH

K

J

a. ASA; CPCTC c. AAS; CPCTC b. ASA; Substitution d. SAS; CPCTC

____ 62. In an A-frame house, the two congruent sides extend from the ground to form a 34° angle at the peak. What

angle does each side form with the ground? a. 146 b. 156 c. 78 d. 73

____ 63. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 34° and the two

congruent sides each measure 21 units?

34°

Drawing not to scale

2121

a. 146° b. 156° c. 78° d. 73°

____ 64. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 34°?

a. 112° b. 73° c. 68° d. 146°

____ 65. B is the midpoint of D is the midpoint of and AE = 21. Find BD. The diagram is not to scale.

A E

C

B D

a. 10.5 b. 21 c. 11.5 d. 42

____ 66. Points B, D, and F are midpoints of the sides of EC = 45 and DF = 16. Find AC. The diagram is not

to scale.

EC

A

D

FB

a. 32 b. 45 c. 90 d. 8

____ 67. Use the information in the diagram to determine the height of the tree. The diagram is not to scale.

a. 90 ft b. 43 ft c. 45 ft d. 180 ft

____ 68. Find the value of x.

16

2x – 6

a. 9 b. 7 c. 11 d. 8

____ 69. Name a median for

E D

C

H

F G

|

|

))

a. b. c. d.

____ 70. Find the length of , given that is a median of the triangle and AC = 60.

A C

D

B

a. 30 c. 120 b. 60 d. not enough information

____ 71. What is the name of the segment inside the large triangle?

a. perpendicular bisector c. median b. midsegment d. angle bisector

____ 72. List the sides in order from shortest to longest. The diagram is not to scale.

J

L

K

32°

55°

93°

a. b. c. d.

____ 73. ABCD is a parallelogram. If then The diagram is not to scale.

A B

D C

a. 126 b. 116 c. 64 d. 128

____ 74. WXYZ is a parallelogram. Name an angle congruent to

X

ZW

Y

N

a. b. c. d.

____ 75. In the parallelogram, and Find The diagram is not to scale.

J

LM

K

O

a. 46 b. 101 c. 55 d. 91

Review for Final - Geometry A Answer Section

MULTIPLE CHOICE

1. A

2. A

3. A

4. A

5. A

6. A

7. D

8. C

9. C

10. C

11. D

12. A

13. B

14. D

15. A

16. D

17. C

18. A

19. A

20. C

21. C

22. D

23. D

24. D

25. C

26. A

27. D

28. A

29. B

30. B

31. C

32. A

33. B

34. C

35. A

36. A

37. B

38. C

39. D

40. A

41. B

42. C

43. D

44. A

45. D

46. D

47. D

48. B

49. B

50. A

51. D

52. D

53. B

54. A

55. C

56. D

57. B

58. B

59. A

60. D

61. A

62. D

63. D

64. A

65. A

66. A

67. A

68. B

69. D

70. A

71. D

72. A

73. B

74. B

75. B