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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