Name: ________________________ Class: ___________________ Date: __________ ID: A

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Honors Geometry Mid-Term Exam Review

Multiple Choice

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

1. Classify the triangle by its sides. The diagram is

not to scale.

a. straight b. equilateral c. isosceles

d. scalene

2. Find the perimeter of the rectangle. The drawing is

not to scale.

a. 158 feet b. 79 feet c. 107 feet d. 130 feet

3. Supplementary angles are two angles whose

measures have sum ____.

Complementary angles are two angles whose

measures have sum ____.

a. 90; 180 b. 180; 90 c. 90; 45 d. 180; 360

4. Find the values of a and b.The diagram is not to

scale.

a. a = 126, b = 54 b. a = 126, b = 50

c. a = 130, b = 54 d. a = 130, b = 50

5. DF→

bisects ∠EDG. Find FG. The diagram is not to

scale.

a. 23 b. 22 c. 44 d. 27

6. The complement of an angle is 59°. What is the

measure of the angle?

a. 41° b. 131° c. 31° d. 121°

7. Which statement is an example of the Subtraction

Property of Equality?

a. If c = d then c + e = d + e b. c = d c. If

c = d then c ⋅ e = d ⋅ e d. If c = d then

c − e = d − e.

8. Find the distance between points P(7, 1) and Q(4,

6) to the nearest tenth.

a. 34 b. 8 c. 5.8 d. 13

Name: ________________________ ID: A

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9. List the sides in order from shortest to longest. The

diagram is not to scale.

a. JK , LJ , LK b. JK , LK , LJ c. LK , JK , LJ

d. LK , LJ , JK

10. Find the value of x.

a. 5 b. 7 c. 9 d. 9.5

11. LMNO is a parallelogram. If NM = x + 9 and OL =

2x + 6 find the value of x and then find NM and

OL.

a. x = 3, NM = 14, OL = 12 b. x = 5, NM = 12,

OL = 14 c. x = 3, NM = 12, OL = 12 d. x = 5,

NM = 14, OL = 14

12. What is the measure of a base angle of an isosceles

triangle if the vertex angle measures 38° and the

two congruent sides each measure 21 units?

a. 71° b. 152° c. 142° d. 76°

13. Complete the statement. If a transversal intersects

two parallel lines, then ____.

a. same-side interior angles are complementary

b. alternate interior angles are congruent

c. corresponding angles are supplementary

d. none of these

14. Find the values of x and y.

a. x = 90, y = 56 b. x = 90, y = 34

c. x = 34, y = 56 d. x = 56, y = 34

Name: ________________________ ID: A

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15. Line r is parallel to line t. Find m∠5. The diagram

is not to scale.

a. 146 b. 24 c. 34 d. 134

16. If T is the midpoint of SU , find the values of x and

ST. The diagram is not to scale.

a. x = 19, ST = 75 b. x = 14, ST = 56 c. x = 14,

ST = 75 d. x = 19, ST = 56

17. Write an equation in point-slope form, y – y1 = m(x

– x1), of the line through points (10, –8) and (9, 2)

Use (10, –8) as the point (x1, y1).

a. (y + 8) = –10(x – 10) b. (y – 8) = –10(x + 10)

c. (y + 8) = 10(x – 10) d. (y – 8) = 10(x + 10)

18. Find the value of the variable. The diagram is not

to scale.

a. 61 b. 12 c. 41 d. 22

19. Justify the last two steps of the proof.

Given: PQ ≅ SR and PR ≅ SQ

Prove: ∆PQR ≅ ∆SRQ

Proof:

1. PQ ≅ SR 1. Given

2. PR ≅ SQ 2. Given

3. QR ≅ RQ 3. ?

4. ∆PQR ≅ ∆SRQ 4. ?

a. Reflexive Property of ≅; SAS b. Symmetric

Property of ≅; SAS c. Symmetric Property of ≅;

SSS d. Reflexive Property of ≅; SSS

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

a. 40 b. 100 c. 68 d. 80

Name: ________________________ ID: A

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21. What is the intersection of plane TUYX and plane

VUYZ?

a. TX→←

b. VZ→←

c. UY→←

d. SW→←

22. Which three lengths can NOT be the lengths of the

sides of a triangle?

a. 10 m, 12 m, 10 m b. 16 m, 5 m, 11 m c. 6

m, 10 m, 8 m d. 24 m, 19 m, 15 m

23. Jay, Kay, and Ray found themselves far apart when

they stopped for lunch while working in a field. Jay

could see Kay, then turn through 66° and see Ray.

Kay could see Ray, then turn through 54° and see

Jay. Ray could see Jay, then turn through 60° and

see Kay. Which two were farthest apart?

a. Ray and Jay b. Kay and Ray c. Jay and Kay

d. Kay and Ray were the same distance apart as

Ray and Jay.

24. The sides of an isosceles triangle have lengths

2x + 2, x + 5. The base has length 2x + 6. What is

the length of the base?

a. 8 b. 3 c. 12 d. cannot be determined

25. A triangle has side lengths of 14 cm, 48 cm, and 50

cm. Classify it as acute, obtuse, or right.

a. right b. obtuse c. acute

26. Name the smallest angle of ∆ABC. The diagram is

not to scale.

a. Two angles are the same size and smaller than

the third. b. ∠B c. ∠A d. ∠C

27. Q is equidistant from the sides of ∠TSR. Find the

value of x. The diagram is not to scale.

a. 13 b. 4 c. 34 d. 17

Name: ________________________ ID: A

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Fill in each missing reason.

28. Given: m∠PQR = x + 7, m∠SQR = x + 3, and m∠PQS = 100.

Find x.

m∠PQR + m∠SQR = m∠PQS a. _____

x + 7 + x + 3 = 100 b. Substitution Property

2x + 10 = 100 c. Simplify

2x = 90 d. _____

x = 45 e. Division Property of Equality

a. Angle Addition Postulate; Subtraction Property of Equality b. Protractor Postulate; Addition Property of

Equality c. Angle Addition Postulate; Addition Property of Equality d. Protractor Postulate; Subtraction

Property of Equality

29. Given: 8x − 5y = 1; x = −2

Prove: −17

5= y

8x − 5y = 1; x = −2 a. ________

−16 − 5y = 1 b. ________

−5y = 17 c. ________

y =−17

5d. ________

−17

5= y e. ________

a. a. Given

b. Substitution Property

c. Addition Property of Equality

d. Division Property of Equality

e. Symmetric Property of Equality

c. a. Given

b. Substitution Property

c. Addition Property of Equality

d. Division Property of Equality

e. Reflexive Property of Equality

b. a. Given

b. Substitution Property

c. Addition Property of Equality

d. Addition Property of Equality

e. Symmetric Property of Equality

d. a. Given

b. Symmetric Property of Equality

c. Addition Property of Equality

d. Division Property of Equality

e. Reflexive Property of Equality

Name: ________________________ ID: A

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30. If ∠A ≅ ∠D and ∠C ≅ ∠F, which additional statement does NOT allow you to conclude that ∆ABC ≅ ∆DEF?

a. BC ≅ EF b. AB ≅ EF c. ∠B ≅ ∠E d. AC ≅ DF

31. Given ∆QRS ≅ ∆TUV, QS = 5v + 2, and

TV = 7v − 8, find the length of QS and TV.

a. 28 b. 27 c. 43 d. 5

32. Which three lengths could be the lengths of the

sides of a triangle?

a. 19 cm, 6 cm, 6 cm b. 13 cm, 9 cm, 22 cm

c. 9 cm, 25 cm, 10 cm d. 10 cm, 13 cm, 22 cm

33. DEFG is a rectangle. DF = 3x – 5 and EG = x + 15.

Find the value of x and the length of each diagonal.

a. x = 5, DF = 20, EG = 20 b. x = 10, DF = 20,

EG = 20 c. x = 10, DF = 25, EG = 28 d. x = 10,

DF = 25, EG = 25

34. In the figure shown, m∠AED = 120. Which of the

following statements is false?

Not drawn to scale

a. ∠DEC and ∠DEA are vertical angles.

b. ∠DEA and ∠AEB are adjacent angles.

c. m∠AEB = 60 d. m∠BEC = 120

35. Noam wants to put a fence around his rectangular

garden. His garden measures 31 feet by 36 feet.

The garden has a path around it that is 3 feet wide.

How much fencing material does Noam need to

enclose the garden and path?

a. 110 ft b. 158 ft c. 79 ft d. 146 ft

36. Find AM in the parallelogram if PN =10 and AO =

6. The diagram is not to scale.

a. 12 b. 6 c. 5 d. 10

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

a. x = 22 b. x = 50 c. x = 14 d. none of

these

Name: ________________________ ID: A

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38. Name the three labeled segments that are parallel to

BF .

a. DH , GH , AE b. CD, AE, DH c. FH , CG,

AE, d. CG, AE, DH

39. Use the information in the diagram to determine

the height of the tree. The diagram is not to scale.

a. 32.5 ft b. 65 ft c. 130 ft d. 30.5 ft

40. Find the missing angle measures. The diagram is

not to scale.

a. x = 115, y = 123 b. x = 66, y = 115 c. x =

66, y = 105 d. x = 105, y = 66

41. Write an equation for the line perpendicular to y =

–2x – 13 that contains (1, –10).

a. y + 10 = 1

2(x – 1) b. y + 10 = –2(x – 1) c. x

+ 10 = –2(y – 1) d. y + 1 = 1

2(x – 10)

42. The sum of the measures of two exterior angles of

a triangle is 277. What is the measure of the third

exterior angle?

a. 83 b. 73 c. 97 d. 93

43. Find the values of the variables in the

parallelogram. The diagram is not to scale.

a. x = 39, y = 27, z = 114 b. x = 27, y = 27,

z = 153 c. x = 39, y = 27, z = 153 d. x = 27,

y = 39, z = 114

44. Find the values of x and y.

a. x = 120, y = 60 b. x = 60, y = 120 c. x

= 30, y = 41 d. x = 41, y = 30

45. If m∠EOF = 32 and m∠FOG = 36, then what is

the measure of ∠EOG? The diagram is not to scale.

a. 4 b. 64 c. 68 d. 72

Name: ________________________ ID: A

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46. Find the values of x, y, and z. The diagram is not to

scale.

a. x = 78, y = 102, z = 62

b. x = 62, y = 102, z = 78

c. x = 78, y = 62, z = 102

d. x = 62, y = 78, z = 102

47. Find the value of x.

a. 103 b. 19 c. –19 d. 77

48. If BCDE is congruent to OPQR, then BE is

congruent to ? .

a. OP b. OR c. PQ d. QR

49. Name the theorem or postulate that lets you

immediately conclude ∆ABD ≅ ∆CBD.

a. ASA b. AAS c. SAS d. none of these

50. A triangle has sides of lengths 12, 14, and 19. Is it a

right triangle? Explain.

a. no; 122+ 14

2≠ 19

2 b. yes;

122+ 14

2≠ 19

2 c. yes; 12

2+ 14

2= 19

2

d. no; 122+ 14

2= 19

2

51. If EF = 2x − 12, FG = 3x − 13, andEG = 25, find

the values of x, EF, and FG. The drawing is not to

scale.

a. x = 10, EF = 32, FG = 43 b. x = 1, EF = –10,

FG = –10 c. x = 10, EF = 8, FG = 17 d. x = 1,

EF = 8, FG = 17

52. Are U , V , and W collinear? If so, name the line on which they lie.

a. No, the three points are not collinear. b. Yes, they lie on the line UX . c. Yes, they lie on the line V X .

d. Yes, they lie on the line UW .

Name: ________________________ ID: A

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53. Which statement is true?

a. All quadrilaterals are squares. b. All

quadrilaterals are parallelograms. c. All

rectangles are squares. d. All squares are

quadrilaterals.

54. Find the length of AB, given that DB is a median of

the triangle and AC = 56.

a. 56 b. 28 c. 112 d. not enough information

55. ABCD is a parallelogram. If m∠CDA = 59, then

m∠DAB = ? . The diagram is not to scale.

a. 118 b. 121 c. 59 d. 131

56. Name a median for ∆ABC.

a. BD b. AD c. CE d. AF

57. Find the values of the variables and the lengths of

the sides of this kite.

a. x =14, y = 8; 10, 10 b. x = 8, y = 14; 4, 16

c. x =14, y = 8; 4, 16 d. x = 8, y = 14; 10, 20

58. Classify the polygon by its sides.

a. octagon b. hexagon c. pentagon

d. quadrilateral

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

a. 21 b. 115 c. 109 d. 71

60. Name the Property of Congruence that justifies the

statement:

If ST ≅ UV , thenUV ≅ ST .

a. Symmetric Property b. Transitive Property

c. Reflexive Property d. none of these

Name: ________________________ ID: A

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61. What is the name of the segment inside the large

triangle?

a. perpendicular bisector b. median

c. angle bisector d. midsegment

62. Name the Property of Congruence that justifies the statement:

If ∠D ≅ ∠E and ∠E ≅ ∠F, then ∠D ≅ ∠F .

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

63. Supply the missing reasons to complete the proof.

Given: ∠P ≅ ∠S and PR ≅ SR

Prove: QR ≅ TR

Statement Reasons

1.∠P ≅ ∠S and

PR ≅ SR

1. Given

2. ∠QRP ≅ ∠TRS 2. Vertical angles are congruent.

3. ∆QRP ≅ ∆TRS 3. ?

4. QR ≅ TR 4. ?

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

64. Write an equation in slope-intercept form of the

line through point P(–2, 8) with slope 2.

a. y = 2x + 12 b. y – 8 = 2(x + 2) c. y = 2x + 8

d. y – 2 = 2(x + 8)

Name: ________________________ ID: A

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65. Complete the statement. If a transversal intersects

two parallel lines, then ____ angles are

supplementary.

a. same-side interior b. corresponding

c. alternate interior d. acute

66. In each pair of triangles, parts are congruent as

marked. Which pair of triangles is congruent by

ASA?

a.

b.

c.

d.

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

a. 148 b. 73 c. 165 d. 32

68. ∠1 and ∠2 are supplementary angles.

m∠1 = x − 13, and m∠2 = x + 93. Find the measure

of each angle.

a. ∠1 = 50, ∠2 = 130 b. ∠1 = 50, ∠2 = 140

c. ∠1 = 37, ∠2 = 153 d. ∠1 = 37, ∠2 = 143

69. Points B, D, and F are midpoints of the sides of

∆ACE. EC = 32 and DF = 25. Find AC. The

diagram is not to scale.

a. 64 b. 12.5 c. 50 d. 32

70. A model is made of a car. The car is 9 feet long and

the model is 6 inches long. What is the ratio of the

length of the car to the length of the model?

a. 18 : 1 b. 1 : 18 c. 9 : 6 d. 6 : 9

71. Red and grey bricks were used to build a decorative

wall. The number of red bricks

number of grey bricks was

5

2. There

were 175 bricks used in all. How many red bricks

were used?

a. 25 b. 125 c. 50 d. 35

Name: ________________________ ID: A

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What is the solution of each proportion?

72. 6

a=

18

27

a. 54 b. 81 c. 9 d. 18

73. 3y − 8

12=y

5

a. −10 b. −7 c. 3

40 d.

40

3

74. Given the proportion a

b=

8

15, what ratio completes

the equivalent proportion a

8= ?

a. 15

b b.

b

15 c.

8

15 d.

a

15

The polygons are similar, but not necessarily drawn to scale. Find the value of x.

75.

a. x = 8 b. x = 11

2 c. x = 9 d. x = 10

76. Are the two triangles similar? How do you know?

a. yes, by SAS∼ b. yes, by SSS∼ c. yes, by

AA∼ d. no

Name: ________________________ ID: A

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

Given: MO→

bisects ∠PMN and OM→

bisects ∠PON

Prove: ∆PMO ≅ ∆MNO

Statements Reasons

1. MO→

bisects ∠PMN 1. Given

2. ∠PMO ≅ ∠NMO 2. Definition of angle bisector

3. MO ≅ MO 3. Reflexive property

4. OM→

bisects ∠PON 4. Given

5. ∠POM ≅ ∠NOM 5. Definition of angle bisector

6. ∆PMO ≅ ∆NMO 6. ?

a. ASA Postulate b. SSS Postulate c. SAS Postulate d. AAS Theorem

78. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to

scale.

a. x = 9, y = 18 b. x = 8, y = 9 c. x = 9, y = 8 d. x = 9, y = 33

Name: ________________________ ID: A

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79. Supply the reasons missing from the proof shown below.

Given: AB ≅ AC, ∠BAD ≅ ∠CAD

Prove: AD bisects BC

Statements Reasons

1. AB ≅ AC 1. Given

2.∠BAD ≅ ∠CAD 2. Given

3. AD ≅ AD 3. Reflexive Property

4. ∆BAD ≅ ∆CAD 4. ?

5. BD ≅ CD 5. ?

6. AD bisects BC 6. Def. of segment bisector

a. ASA; CPCTC b. SAS; CPCTC c. SSS; Reflexive Property d. SAS; Reflexive Property