MIDTERM EXAM STUDY GUIDE (GEOMETRY)
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
47. If two polygons are SIMILAR, then the
corresponding angles must be _____.
51. In the figure shown, PQ = 32 centimeters, ST = 8
centimeters, and m  QRP = 65 . Find m S .
[A] complementary
[B] linear pairs
[A] 65
[B] 115
[C] supplementary
[D] congruent
[C] 25
[D] 100
P
Q
R
T
S
48. If two polygons are SIMILAR, then the
corresponding sides must be _____.
52. One way to show that two triangles are similar is to
show that ______.
[A] parallel
[B] congruent
[A] two sides of one are proportional to two sides of
the other
[C] similar
[D] proportional
[B] a side of one is congruent to a side of the other
49. Given that ABC ~ DEF , solve for x and y.
A
[D] two angles of one are congruent to two angles of
the other
D
21
y
x
10
B
12
C
[C] an angle of one is congruent to an angle of the
other
E
7
F
53. Two ladders are leaning against a wall at the same
angle as shown.
[A] x  12.25, y  17.14
[B] x  1125
. , y  17.14
[C] x  12.25, y  1614
.
72 ft
48 ft
[D] x  1125
. , y  1614
.
50. If  ABC ~  DEF and  DEF ~  GHI,
then ______.
24 ft
[A]  BCA   GHI
[B]  ABC   GHI
How far up the wall does the shorter ladder reach?
[C]  ABC ~  GHI
[A] 12 ft
[B] 32 ft
[C] 16 ft
[D] 14 ft
[D] AB = GH
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
54. Two ladders are leaning against a wall at the same
angle as shown. How long is the shorter ladder?
56. The postulate or theorem that can be used to prove
that the two triangles are similar is _____.
[A] SSS Similarity Theorem
42 ft
30 ft
[B] AA Similarity Postulate
[C] SAS Similarity Theorem
10 ft
[A] 14 ft
[D] ASA Congruence Theorem
57. Given: PQ || BC . Find the length of AB .
A
[B] 8 ft
10
[C] 18 ft
P
15
Q
24
[D] 28 ft
B
55. Shown below is an illustration of the ______.
C
[A] 28
[B] 26
[C] 23
[D] 22
58. Find the value of x to one decimal place.
[A] SAS Similarity Theorem
[B] SAS Congruence Theorem
[C] SSS Similarity Theorem
[A] 19.0
[D] AA Similarity Postulate
[B] 2.2
[C] 22.5
[D] 0.5
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
59. If  ABC ~  PBQ, then which of the following
proportions is NOT true?
[A]
AP
CQ

PB
QB
[B]
PB
PQ

AB
AC
[C]
AP
AC

PB
PQ
61. Dawn is laying computer cables in the ceiling of a
large building. A 200-ft cable to office B1 and a 480-ft
cable to office B2 meet at a right angle. Offices B1 and
B2 are both on the outer wall of the building. If Dawn
lays one cable from where the first two cables meet
directly to the outer wall, how far will it be from there
to office B1? Round your answer to the nearest tenth.
[A] 65.1 ft
[B] 260.0 ft
[C] 76.9 ft
[D]
AC
CB

PQ
QB
[D] 520.0 ft
60. Which image does not show a dilation?
[A]
62. Find the value of x.
[A] 4 15
x
[B] 4 6
8
12
[C] 2 5
[B]
[D] 4 10
[C]
63. Find the length of the leg of this right triangle. Give
an approximation to 3 decimal places.
[A] 21.260
[B] 7.071
[D]
16
[C] 7.746
14
[D] 8.067
a
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
64. How long is a string reaching from the top of a 16ft pole to a point 7 ft from the base of the pole?
[A]
207 ft
[B]
305 ft
67. A telephone pole breaks and falls as shown.
6 ft
[C]
217 ft
[D]
315 ft
11 ft
To the nearest foot, what was the original height of the
pole?
65. The city commission wants to construct a new
street that connects Main Street and North Boulevard
as shown in the diagram below. The construction cost
has been estimated at $80 per linear foot. Find the
estimated cost for constructing the street. (1 mile =
5280 ft)
North Blvd.
[A] $3,894,336
(new street)
[B] $48,679
7 mi
[A] 17 ft
[B] 18 ft
[C] 20 ft
[D] 19 ft
68. ABC is a right triangle. AB = _____.
[A] 3 6
[C] $3,938,780
W
[D] $422,400
Main St. E
[B] 3 13
S
[C] 117
6 mi
[D] 3 5
66. A radio station is going to construct a 6-foot tower
for a new antenna. The tower will be supported by
three cables, each attached to the top of the tower and
to points on the roof of the building that are 8 feet from
the base of the tower. Find the total length of the three
cables.
[A] 10 ft
69. For the triangle shown below, the Pythagorean
Theorem states that _____.
[A] f 2 – g 2  e2
[B] e2  f 2  g 2
[B] 50 ft
[C] e = f + g
[C] 40 ft
[D] 30 ft
[D] e2  f 2  g 2
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
70. A 25.5 foot ladder rests against the side of a house
at a point 24.1 feet above the ground. The foot of the
ladder is x feet from the house. Find the value of x to
one decimal place.
72. An equilateral triangle has side lengths of 10. The
length of its altitude is _____.
[A] 8.3
[B] 5
[B] 1.9
25.5 ft
24.1
ft
[C] 7.0
[A] 5 10
[C] 5 3
[D] 10 5
[D] 10.1
x
73. Write cos A.
71. Which triangle below is NOT congruent to the
others?
[A]
5
4
[A]
4
5
B
5
3
[B]
4
A
3
[C]
3
5
[D]
4
3
[B]
4
3
C
30
3
74. The tangent of B is _____.
[C]
3
[A] 7 95
[B]
5
[C]
[D]
95
12
12
7
3
[D]
4
95
7
MIDTERM EXAM STUDY GUIDE (GEOMETRY)
75. To find the height of a tower, a surveyor positions a
transit that is 2 m tall at a spot 90 m from the base of
the tower. She measures the angle of elevation to the
top of the tower to be 35  . What is the height of the
tower, to the nearest meter?
79. Solve for x to the nearest degree.
[A] 129 m
[C] 19
[B] 131 m
[D] 69
[A] 71
[B] 21
6
x°
17
[C] 65 m
[D] 63 m
80. Which of the following is NOT enough information
to solve a right triangle?
76. A slide 5.2 m long makes an angle of 35  with the
ground. How high is the top of the slide above the
ground?
[A] One side length and one trigonometric ratio
[B] One side length and one acute angle measure
[A] 3.64 m
[C] Two sides
[B] 4.26 m
[D] Two angles
[C] 3.17 m
[D] 2.98 m
81. Use your calculator to determine cos 23°.
77. Liola drives 18 km up a hill that is at a grade of
10. What horizontal distance, to the nearest tenth of
kilometer, has she covered?
[A] 3.2 km
[B] 3.1 km
[C] 17.7 km
[D] 9.5 km
[A]  0.921
[B]  1.07
[C]  0.390
[D]  0.424
78. What is x to the nearest hundredth? (not drawn to
scale)
[A] x = 9.26
17
[B] x = 2618
.
[C] x = 14.26
[D] x = 1104
.
x
33°