Semester Exam Review

Multiple Choice

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

____ 1. Are O, N, and P collinear? If so, name the line on which they lie.

M

N

O

P

a. No, the three points are not collinear.

b. Yes, they lie on the line MP.

c. Yes, they lie on the line NP.

d. Yes, they lie on the line MO.

____ 2. Name the plane represented by the front of the box.

a. FBC b. BAD c. FEC d. FKG

____ 3. Are points B, J, and C collinear or noncollinear?

a. collinear b. noncollinear c. impossible to tell

____ 4. Name the line and plane shown in the diagram.

T

U

R

S

a.

and plane RSU c.

and plane UR

b. line R and plane RSU d. and plane UT

____ 5. What is the intersection of plane TUYX and plane VUYZ?

a.

b.

c.

d.

____ 6. Name the intersection of plane BPQ and plane CPQ.

a.

c.

b.

d. The planes need not intersect.

____ 7. Name a fourth point in plane TUW.

a. Y b. Z c. W d. X

____ 8. ____ two points are collinear.

a. Any b. Sometimes c. No

____ 9. Plane ABC and plane BCE ____ be the same plane.

a. must b. may c. cannot

____ 10. and ____ be coplanar.

a. must b. may c. cannot

____ 11. Which diagram shows plane PQR and plane QRS intersecting only in ?

a. c.

b. d.

____ 12. Name the ray in the figure.

A B

a.

b.

c. d.

____ 13. Name the ray that is opposite

A

B

C

D

a.

b.

c.

d.

____ 14. Name the four labeled segments that are skew to

a. , , , c. , , ,

b. , , , d. , , ,

____ 15. Name the three labeled segments that are parallel to

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

____ 16. How many pairs of skew lines are shown?

a. 24 b. 12 c. 48 d. 4

____ 17. Which plane is parallel to plane EFHG?

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

____ 18. Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth.

a. 11 b. 7.8 c. 61 d. 14.9

____ 19. The Frostburg-Truth bus travels from Frostburg Mall through the City Center to Sojourner Truth Park. The

mall is 3 miles west and 2 miles south of the City Center. Truth Park is 4 miles east and 5 miles north of the

Center. How far is it from Truth Park to the Mall to the nearest tenth of a mile?

a. 9.9 miles b. 3.6 miles c. 3.2 miles d. 6.4 miles

____ 20. A high school soccer team is going to Columbus to see a professional soccer game. A coordinate grid is

superimposed on a highway map of Ohio. The high school is at point (3, 4) and the stadium in Columbus is at

point (7, 1). The map shows a highway rest stop halfway between the cities. What are the coordinates of the

rest stop? What is the approximate distance between the high school and the stadium? (One unit 6.4 miles.)

a. , 5 miles

c. , 32 miles

b. , 160 miles

d. , 16 miles

____ 21. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside?

OceanfrontLandview

Seaside

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

a. about 10 miles c. about 8 miles

b. about 50 miles d. about 40 miles

____ 22. Find the coordinates of the midpoint of the segment whose endpoints are H(8, 2) and K(6, 10).

a. (7, 6) b. (1, 4) c. (14, 12) d. (2, 8)

____ 23. Find the midpoint of

P

Q

5 10–5–10 x

5

10

–5

–10

y

a. (–3, –1) b. (–2, 0) c. (–2, –1) d. (–3, 0)

____ 24. M(9, 8) is the midpoint of The coordinates of S are (10, 10). What are the coordinates of R?

a. (9.5, 9) b. (11, 12) c. (18, 16) d. (8, 6)

____ 25. M is the midpoint of for the points C(3, 4) and F(9, 8). Find MF.

a. 13 b. 2 13 c. 26 d. 13

____ 26. Write the two conditional statements that make up the following biconditional.

I drink juice if and only if it is breakfast time.

a. I drink juice if and only if it is breakfast time.

It is breakfast time if and only if I drink juice.

b. If I drink juice, then it is breakfast time.

If it is breakfast time, then I drink juice.

c. If I drink juice, then it is breakfast time.

I drink juice only if it is breakfast time.

d. I drink juice.

It is breakfast time.

____ 27. One way to show that a statement is NOT a good definition is to find a ____.

a. converse c. biconditional

b. conditional d. counterexample

____ 28. Use the Law of Detachment to draw a conclusion from the two given statements.

If two angles are congruent, then they have equal measures.

and are congruent.

a. + = 90 c. is the complement of .

b. = d.

____ 29. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not

possible.

I can go to the concert if I can afford to buy a ticket.

I can go to the concert.

a. I can afford to buy a ticket.

b. I cannot afford to buy the ticket.

c. If I can go to the concert, I can afford the ticket.

d. not possible

____ 30. Which statement is the Law of Detachment?

a. If is a true statement and q is true, then p is true.

b. If is a true statement and q is true, then is true.

c. If and are true, then is a true statement.

d. If is a true statement and p is true, then q is true.

____ 31. If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible,

write not possible.

Statement 1: If x = 3, then 3x – 4 = 5.

Statement 2: x = 3

a. 3x – 4 = 5 c. If 3x – 4 = 5, then x = 3.

b. x = 3 d. not possible

____ 32. 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. If a number is a multiple of 64, then it is a multiple of 2.

b. The number is a multiple of 2.

c. The number is a multiple of 8.

d. If a number is not a multiple of 2, then the number is not a multiple of 64.

____ 33. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements.

If an elephant weighs more than 2,000 pounds, then it weighs more than Jill’s car.

If something weighs more than Jill’s car, then it is too heavy for the bridge.

Smiley the Elephant weighs 2,150 pounds.

a. Smiley is too heavy for the bridge.

b. Smiley weighs more than Jill’s car.

c. If Smiley weighs more than 2000 pounds, then Smiley is too heavy for the bridge.

d. If Smiley weighs more than Jill’s car, then Smiley is too heavy for the bridge.

____ 34. Which statement is the Law of Syllogism?

a. If is a true statement and p is true, then q is true.

b. If is a true statement and q is true, then p is true.

c. if and are true statements, then is a true statement.

d. If and are true statements, then is a true statement.

____ 35. Find the values of x, y, and z. The diagram is not to scale.

38°

56°

19°

x° y°z°

a. c.

b. d.

____ 36. Find the value of x. The diagram is not to scale.

105°

72°

x°

a. 33 b. 162 c. 147 d. 75

____ 37. Find the value of the variable. The diagram is not to scale.

114°

47°x°

a. 66 b. 19 c. 29 d. 43

____ 38. Find the missing values of the variables. The diagram is not to scale.

x°

y°124° 65°

125°

a. x = 124, y = 125 c. x = 114, y = 56

b. x = 56, y = 114 d. x = 56, y = 124

____ 39. Graph y = 3

4x – 1.

a.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y c.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

b.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y d.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

____ 40. Graph .

a.

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

c.

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

b.

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

d.

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

____ 41. Write an equation in point-slope form of the line through point J(–5, 6) with slope –4.

a. c.

b. d.

____ 42. Write an equation in point-slope form of the line through points (4, –4) and (1, 2). Use (4, –4) as the point (x1,

y1).

a. (y – 4) = –2(x + 4) c. (y + 4) = 2(x – 4)

b. (y – 4) = 2(x + 4) d. (y + 4) = –2(x – 4)

____ 43. Write an equation for the horizontal line that contains point E(–3, –1).

a. x = –1 b. x = –3 c. y = –1 d. y = –3

____ 44. Graph the line that goes through point (–5, 5) with slope 1

5.

a.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

c.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

b.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

d.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

____ 45. Write an equation in slope-intercept form of the line through point P(–10, 1) with slope –5.

a. y = –5x – 49 c. y – 10 = –5(x + 1)

b. y – 1 = –5(x + 10) d. y = –5x + 1

____ 46. Write an equation in slope-intercept form of the line through points S(–10, –3) and T(–1, 1).

a.

4

9x +

13

9

c.

4

9x –

13

9

b. y =

4

9x –

13

9

d. y =

4

9x +

13

9

____ 47. Write an equation for the line parallel to y = –7x + 15 that contains P(9, –6).

a. x + 6 = 7(y – 9) c. y – 6 = –7(x – 9)

b. y + 6 = 7(x – 9) d. y + 6 = –7(x – 9)

____ 48. Is the line through points P(1, 9) and Q(9, 6) perpendicular to the line through points R(–6, 0) and S(–9, 8)?

Explain.

a. Yes; their slopes have product –1.

b. No, their slopes are not opposite reciprocals.

c. No; their slopes are not equal.

d. Yes; their slopes are equal.

____ 49. Write an equation for the line perpendicular to y = 2x – 5 that contains (–9, 6).

a. y – 6 = 2(x + 9) c. y – 9 =

1

2(x + 6)

b. x – 6 = 2(y + 9) d. y – 6 =

1

2(x + 9)

____ 50. Are the lines y = –x – 2 and 4x + 4y = 16 perpendicular? Explain.

a. Yes; their slopes have product –1.

b. No; their slopes are not opposite reciprocals.

c. Yes; their slopes are equal.

d. No; their slopes are not equal

____ 51. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?

a.

c.

b.

d.

____ 52. Can you use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent?

a. either ASA or AAS c. AAS only

b. ASA only d. neither

____ 53. What else must you know to prove the triangles congruent by ASA? By SAS?

A

CD

B

(

(

a. ; c. ;

b. ; d. ;

____ 54. Based on the given information, what can you conclude, and why?

Given:

I

L

K

H

J

a. by ASA c. by ASA

b. by SAS d. by SAS

____ 55. Find the values of x and y.

A

DB C

||

((

47°

Drawing not to scale

y°

x°

a. c.

b. d.

____ 56. Find the value of x. The diagram is not to scale.

40

40

25 25

32

x

a. 32 b. 50 c. 64 d. 80

____ 57. The length of is shown. What other length can you determine for this diagram?

F

DG

E

|

|

12

a. EF = 12 c. DF = 24

b. DG = 12 d. No other length can be determined.

____ 58. bisects Find FG. The diagram is not to scale.

D

F

E

G

))

n + 8

3n – 4

a. 15 b. 14 c. 19 d. 28

____ 59. Find the center of the circle that you can circumscribe about the triangle.

(–3, –2)

(–3, 3)

(1, –2)

5–5 x

5

–5

y

a.

(1

2, 1)

b. (1,

1

2)

c. (–3,

1

2)

d. (1, –2)

____ 60. Where is the center of the largest circle that you could draw inside a given triangle?

a. the point of concurrency of the altitudes of the triangle

b. the point of concurrency of the perpendicular bisectors of the sides of the triangle

c. the point of concurrency of the bisectors of the angles of the triangle

d. the point of concurrency of the medians of the triangle

____ 61. Where can the perpendicular bisectors of the sides of a right triangle intersect?

I. inside the triangle

II. on the triangle

III. outside the triangle

a. I only b. II only c. I or II only d. I, II, or II

____ 62. Where can the bisectors of the angles of an obtuse triangle intersect?

I. inside the triangle

II. on the triangle

III. outside the triangle

a. I only b. III only c. I or III only d. I, II, or II

____ 63. In ACE, G is the centroid and BE = 9. Find BG and GE.

C

FA

D

E

BG

a. BG = 2

1

4, GE = 6

3

4

c.

b. d. BG = 4

1

2, GE = 4

1

2

____ 64. Name a median for

C B

A

F

D E|

|

))

a. b. c. d.

____ 65. For a triangle, list the respective names of the points of concurrency of

• perpendicular bisectors of the sides

• bisectors of the angles

• medians

• lines containing the altitudes.

a. incenter

circumcenter

centroid

orthocenter

b. circumcenter

incenter

centroid

orthocenter

c. circumcenter

incenter

orthocenter

centroid

d. incenter

circumcenter

orthocenter

centroid

____ 66. Where can the lines containing the altitudes of an obtuse triangle intersect?

I. inside the triangle

II. on the triangle

III. outside the triangle

a. I only b. I or II only c. III only d. I, II, or II

____ 67. Which diagram shows a point P an equal distance from points A, B, and C?

a.

c.

b.

d.

____ 68. Name the second largest of the four angles named in the figure (not drawn to scale) if the side included by

and is 11 cm, the side included by and is 16 cm, and the side included by and is 14 cm.

1

32 4

a. b. c. d.

____ 69. Name the smallest angle of The diagram is not to scale.

A B

C

5 6

7

a. b. c. Two angles are the same size and smaller than the third.

d.

____ 70. Which three lengths can NOT be the lengths of the sides of a triangle?

a. 23 m, 17 m, 14 m c. 5 m, 7 m, 8 m

b. 11 m, 11 m, 12 m d. 21 m, 6 m, 10 m

____ 71. Two sides of a triangle have lengths 7 and 15. Which inequalities represent the possible lengths for the third

side, x?

a. c. b. d.

____ 72. Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side?

a. less than 25 b. less than 10 c. less than 15 d. less than 5

Short Answer

73. Construct the perpendicular bisector of the segment.

74. Construct the bisector of

75. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, state not

possible. Explain.

Statement 1: If two lines intersect, then they are not parallel.

Statement 2: do not intersect.

76. For the given statements below, write the first statement as a conditional in if-then form. Then, if possible, use

the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not

possible. Explain.

A straight angle has a measure of 180.

is a straight angle.

77. Write the missing reasons to complete the flow proof.

Given: are right angles,

Prove:

) (

A

B

CD

78. Can you conclude the triangles are congruent? Justify your answer.

Essay

79. Write a paragraph proof to show that .

Given: and

B

E

A

D

C

80. Write a two-column proof.

Given: and

Prove:

B

E

A

D

C

81. Write a two-column proof:

Given:

Prove:

B

A

D

C

Other

82. Use indirect reasoning to explain why a quadrilateral can have no more than three obtuse angles.

83. Keegan knows that the statement “if a figure is a rectangle, then it is a square” is false, but he thinks the

contrapositive is true. Is he correct? Explain.

84. Explain why

156

3

4

2

85. P, Q, and R are three different points. PQ = 3x + 2, QR = x, and RP = x + 2, and .. List the angles of

PQR in order from largest to smallest and justify your response.

86. Two sides of a triangle have lengths 6 and 8. What lengths are possible for the third side? Explain.

Semester Exam Review

Answer Section

MULTIPLE CHOICE

1. A

2. A

3. A

4. A

5. A

6. A

7. B

8. A

9. B

10. B

11. C

12. A

13. A

14. A

15. A

16. A

17. A

18. B

19. A

20. C

21. D

22. A

23. C

24. D

25. A

26. B

27. D

28. B

29. D

30. D

31. A

32. A

33. A

34. C

35. D

36. A

37. B

38. C

39. D

40. C

41. D

42. D

43. C

44. D

45. A

46. D

47. D

48. B

49. D

50. B

51. B

52. C

53. B

54. A

55. D

56. C

57. A

58. B

59. B

60. C

61. B

62. A

63. B

64. D

65. B

66. C

67. A

68. A

69. D

70. D

71. D

72. A

SHORT ANSWER

73.

74.

75. Not possible. Explanations may vary. Sample: To use the Law of Detachment, you must know that the

hypothesis is true.

76. If an angle is straight, then its measure is 180.

Conclusion: is 180.

77. a. Definition of right triangles

b. Converse of Isosceles Triangle Theorem

c. Reflexive property

d. Angle-Angle-Side Congruence Theorem

78. Yes, the diagonal segment is congruent to itself, so the triangles are congruent by SAS.

ESSAY

79.

[4] Answers may vary. Sample: You are given that and . Vertical

angles BCA and ECD are congruent, so by SAS.

[3] correct idea, some details inaccurate

[2] correct idea, not well organized

[1] correct idea, one or more significant steps omitted

80. [4]

Statement Reason

1. and 1. Given

2. 2. Vertical angles are congruent.

3. 3. SAS

4. 4. CPCTC

[3] correct idea, some details inaccurate

[2] correct idea, not well organized

[1] correct idea, one or more significant steps omitted

81. [4]

Statement Reason

1. and

1. Given

2. 2. Reflexive Property

3. 3. ASA

4. 4. CPCTC

[3] correct idea, some details inaccurate

[2] correct idea, not well organized

[1] correct idea, one or more significant steps omitted

OTHER

82. Assume a quadrilateral has more than three obtuse angles. Then it has four angles, each with a measure

greater than 90. Their sum is greater than 360, which contradicts the fact that the sum of the measures of the

angles of a quadrilateral is 360. Thus a quadrilateral can have no more than three obtuse angles.

83. No; a statement and its contrapositive are equivalent so they have the same truth value.

84. The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.

85. R, Q, P. Sample: Since x = QR > 0, x < x + 2 < 3x + 2, so QR < RP < PQ. The largest angle (R) is

opposite PQ, the next largest angle (Q) is opposite RP.

86. Let x be the length of the third side. By the Triangle Inequality Theorem,

6 + x > 8, 6 + 8 > x, and 8 + x > 6. Solving each inequality, x > 2, x < 14, and x > –2, respectively, or

2 < x < 14.