GEOMETRY MOCK EXAM
1. What term describes a transformation that does
not change a figure’s size or shape?
6. A regular polygon with n sides is carried onto
itself by a positive rotation about its center that
is a multiple of 60°, but less than 360°.
(A) similarity
Which could NOT be the value of n?
(B) isometry
(A) 3
(C) collinearity
(B) 4
(D) symmetry
(C) 5
(D) 6
For questions 2–4, use the diagram showing
parallelogram ABCD.
7. In the diagram, g h and B lies on line g.
A
E
B
10 cm
I
H
F
5 cm
D
G
C
B
C
2. A reflection across EG carries parallelogram
ABCD onto itself.
A
(A) True
(B) False
g
3. A rotation of 90° about I carries parallelogram
ABCD onto itself.
(A) True
(B) False
4. A rotation of 180° about I carries
parallelogram ABCD onto itself.
(A) True
(B) False
5. Which of these is equivalent to a translation?
h
The figure ABC is reflected across line g, and
its image is reflected across line h. What is the
distance from line g to the final image of point
A?
(A) 5 cm
(B) 15 cm
(C) 20 cm
(D) 25 cm
8. What is the image of the point (–4, 6) under
the transformation T  x, y     y, x  ?
(A) a reflection across one line
(A) (6, 4)
(B) a composition of two reflections across
intersecting lines
(B) (–6, –4)
(C) a composition of two reflections across
parallel lines
(D) (–4, –6)
(C) (4, 6)
9. A figure is rotated about the origin by 180°,
then is translated 4 units right and one unit up.
Which describes the results of the two
transformations?
For questions 13–16, determine if the described
transformation(s) is/are an isometry.
13. A reflection is an isometry.
(A)
 x, y     x  4,  y  1
(A) True
(B)
 x, y     x  4,  y 1
(B) False
(C)
 x, y     y  4, x  1
(D)
 x, y     y  4, x  1
14. A composition of two reflections is an
isometry.
(A) True
10. The point A(4, 3) is rotated –90° about the
origin. In which quadrant is A' ?
(A) I
(B) False
15. A dilation is an isometry.
(B) II
(A) True
(C) III
(B) False
(D) IV
11. A figure is reflected across the line y = 2, then
reflected across the line y = 4. Which single
transformation results in the same image?
16. A composition of a rotation and a dilation is an
isometry.
(A) True
(B) False
(A) a reflection across the line y = 3
(B) a reflection across the line y = 6
(C) a translation 2 units up
(D) a translation 4 units up
12. Point A is the image of point A under a
transformation T. Line  is the perpendicular
bisector of AA at point M. Which describes
the transformation T?
17. In ABC , M is the midpoint of AB and N is
the midpoint of AC . For which type of
1
triangle is MN  BC ?
2
(A) equilateral only
(B) isosceles only
(C) scalene only
(A) a reflection across 
(D) any triangle
(B) a 90° rotation about M
(C) a translation by the vector from A to M
(D) a dilation about M with scale factor 2
18. After a figure is rotated, P  P . Which
statement(s) could be true?
(A) The center of rotation is P.
(B) The angle of rotation is a multiple of
360°.
(C) Either A or B or both.
(D) Neither A nor B.
19. Use the diagram.
m
23. Given point A is located at (1, 3). What is the
final image of A after this series of
transformations?

k
44°
22°
(1) Reflect A across the y axis.
(2) Translate the image such that
 x, y    x  4, y  2 .
(A) (–1, –3)
(B) (–3, 5)
A
(C) (–3, –1)
(D) (–5, 5)
For questions 24–27, use the diagram where B is the
reflection of A across PQ .
Which series of reflections would result in a
rotation of –44° about A?
(A) reflect across k¸ then reflect across 
P
(B) reflect across ¸ then reflect across k
(C) reflect across ¸ then reflect across m
(D) reflect across m¸ then reflect across 
For questions 20–21, a transformation S is defined
as  x, y    3x, y  1 .
20. The pre-image of A  3, 6  under S is A 9, 5 .
(A) True
(B) False
A
24. PA = PB
(A) True
(B) False
25. PQ  AB
(A) True
21. S is an isometry.
(B) False
(A) True
(B) False
26. AQ = QB
(A) True
22. Which transformation does NOT preserve the
orientation of a figure?
(A) dilation
(B) reflection
(B) False
27. PQ 
1
AB
2
(C) rotation
(A) True
(D) translation
(B) False
Q
B
28. Use the figure.
For questions 29–31, use the diagram where ABCD
is a quadrilateral with AB CD and AD BC .
Diagonals AC and BD intersect at E.
B
A
E
A transformation T is defined as
 x, y    x, – y  . Which shows the image of
figure under T?
C
D
29. CBE  ABE
(A) True
(A)
(B) False
30. ADE  ABE
(A) True
(B) False
31. CDE  ABE
(A) True
(B)
(B) False
32. A figure is transformed in the plane such that
no point maps to itself. What type of
transformation must this be?
(A) dilation
(B) reflection
(C)
(C) rotation
(D) translation
For questions 33–36, determine if the mapping is an
isometry.
33.
 x, y    x, y  2 is an isometry.
(A) True
(B) False
34.
 x, y     x, y  is an isometry.
(B) False
 x, y    y, x 
is an isometry.
(A) True
(B) False
36.
39. A rotation of 90° about P results in P = P.
(A) True
(B) False
40. A translation by the vector 6, 0 results in
P = P.
(A) True
35.
For questions 39–41, point P is located at (6, 0) and
undergoes a transformation.
 x, y    2x, y 
(A) True
(B) False
41. A reflection about the x axis results in P = P.
(A) True
(B) False
For questions 42–43, use the diagram which shows
ABC has been reflected across an unknown line ,
then reflected across line m to produce ABC.
y

C
A
is an isometry.
(A) True
(B) False
For questions 37–38, determine the truth of the
statements about rotations.
B
B

 x
A
37. Rotations preserve the orientation of a figure.
(A) True
C

(B) False
38. Under a rotation, no point can map to itself.
m
42. The equation of line  is x = –0.5.
(A) True
(A) True
(B) False
(B) False
43. If ABC were reflected across line m first,
then reflected across line  to produce
ABC, the equation of line  would be x = –
0.5.
(A) True
(B) False
For questions 44–46, consider a triangle ABC
that has been transformed through rigid motions
and its image compared to XYZ . Determine if
the given information is sufficient to draw the
provided conclusion.
44.
Given
A  X
Conclusion
B  Y
C  Z
ABC  XYZ
Look at the figure below.
Look at these three figures.
I
(A) True
(B) False
45.
II
Given
A  X
B  Y
Conclusion
ABC  XYZ
BC  YZ
(A) True
(B) False
46.
Given
A   X
Conclusion
AB  XY
ABC  XYZ
BC  YZ
III
48. Which figures are congruent to the first
figure?
(A) True
(A) I only
(B) False
(B) II only
47. Use the diagram.
s
r
3 4
1 2
(C) I and II only
m
n
8 7
(D) I, II, and III
For questions 49–50, consider ABC where AB =
BC and mA  40 .
6 5
Which statement would be used to prove lines
r and s are parallel?
(A) 1 and 3 are congruent
(B) 2 and 7 are complementary
(C) 4 and 1 are congruent
(D) 8 and 6 are supplementary
49. mB  mC  140
(A) True
(B) False
50. mC  100
(A) True
(B) False
For questions 51–53, evaluate whether the image of
a figure under the described transformation is
congruent to the figure.
51. A transformation T follows the rule
 x, y    x  3, y  . The image of a figure
under T is congruent to the figure.
Use the Venn diagram.
Quadrilaterals
I
Parallelograms
II
Rhombi
Squares
III
IV
Rectangles
V
(A) True
(B) False
Trapezoids VI
VII
Kites
52. A transformation T follows the rule
 x, y     y,  x  . The image of a figure
under T is congruent to the figure.
55. A quadrilateral ABCD has 4 lines of
symmetry. Identify the area of the diagram in
which ABCD resides.
(A) True
(B) False
53. A transformation T follows the rule
 x, y    x, 2 y  . The image of a figure
under T is congruent to the figure.
(A) III
(B) IV
(C) V
(D) VII
(A) True
(B) False
In the diagram, m n and p q .
p
q
m
88°
x°
What is the value of x?
(A) 44
(A) 96 square units
(B) 192 square units
n
54.
56. Right triangle PQR has sides of length 6 units,
8 units, and 10 units. The triangle is dilated by
a scale factor of 4 about point Q. What is the
area of triangle P'Q'R'?
(C) 384 square units
(D) 768 square units
57. The ratio of the side lengths of a triangle is
3:6:8. A second triangle is similar to the first
and its shortest side measures 8.0 centimeters.
What is the length of the longest side of the
second triangle?
(B) 88
(C) 92
(A) 3.0 cm
(D) 176
(B) 10.7 cm
(C) 13.0 cm
(D) 21.3 cm
Use the diagram below.
61. Which figure contains two similar triangles
that are NOT congruent?
A
4
9
H
D
(A)
y
8
B
C
58. What is the value of y?
(B)
(A) 13
(B) 18
(C) 27
(C)
In the diagram, a student has placed a mirror on
level ground, then stands so that the top of a
nearby tree is visible in the mirror.
2m
3m
36 m
(B) 35 m
(B) 41 m
(D) 59 m
(B) The triangles could be similar.
(C) The triangles must be similar.
63. Triangle ABC has vertices A  2, 2  ,
In the diagram, JG QR .
Q
7
P
8
G
x
R
60. What is the value of x?
(A) 11
(B) 6
(C) 5
(D) 3
B  5, 5 , and C  5, 3 . The triangle is
J
4
62. Sally constructs a triangle where two of the
angles measure 50° and 60°. Tom constructs a
triangle where two of the angles measure 50°
and 70°. What is true about the two triangles?
(A) The triangles cannot be similar.
59. What is the height of the tree?
(A) 24 m
(D)
dilated about the point 1, 1 with scale factor
4. What is the location of A' ?
(A)
 8, 8
(B)
 10, 10
(C)
 11, 5
(D)
 14, 6
Use the diagram.
In the diagram, segments AB and CD intersect
at E, F lies on AB , and mAEC  60 .
y

m
B
D
F

E
 x
60°
A

64. Dilate line m about the origin with scale
factor 2. What is the equation of the line’s
image?
C
67. The two segments are dilated about F with
1
scale factor . What is mAEC ?
2
(A) 30°
(B) 60°
(A) y = 2x + 2
(B) y = 2x + 4
(C) 90°
(D) 120°
(C) y = 4x + 2
(D) y = 4x + 4
65. Which is NOT a criterion for triangle
similarity?
68. In the diagram, ABCD is dilated with center O
1
to produce A'B'C'D', and AB  AB .
3
A
(A) angle-angle
(B) angle-side-angle
(C) side-angle-side
D'
(D) side-side
A'
F
D
O
C'
66. J(5, 7) is the image of J(3, 3) after a dilation
with scale factor 3. Where is the center of
dilation?
C
B
(A) (–3, –9)
(B) (0, 0)
What is
(C) (2, 1)
(D) (4, 5)
B'
(A)
1
3
(C) 2
OA
?
AA
(B)
1
2
(D) 3
69. Use the diagram.
Use the right triangle. What is the value of x?
C
b
15
x
a
h
x
8
y
A
D
B
c
Which is equal to h?
(A)
ay
(B)
bx
(C)
xy
(D)
ab
72.
What is the value of x?
(A)
7
(B)
161
(C) 7
(D) 17
73. Consider a triangle ABC. Which statement is
true?
(A) c2  a2  b2  2ab cos C
70. J(5, 7) is the image of J(3, 3) after a dilation
with scale factor 3. Where is the center of
dilation?
(B) c2  a2  b2  2ab cos C
(C) c2  a2  b2  2ab cos C
(D) c2  a2  b2  2ab cos C
(A) (–3, –9)
(B) (0, 0)
(C) (2, 1)
74. Use the diagram.
(D) (4, 5)
A
71. Fred stands at corner A of a rectangular field
shown below. He needs to get to corner C.
A
7
4
B
B
9m
D
9
What is cos A ?
12 m
C
What is the shortest distance from A to C?
(A) 9 m
(B) 13 m
(C) 15 m
(D) 21 m
(A)
16
56
(B)
56
16
(C) 
16
56
(D) 
56
16
C
75. A small airplane flies due north at 150
kilometers per hour. A wind is blowing
towards the direction 60° east of north at 50
kilometers per hour. Which figure represents
the final speed and direction of the airplane?
(A) 
N
(B) 
N
(C) 
N
(D) 
















For questions76-78, consider a triangle ABC and
each given set of measurements.


N

79. The diagram shows a parallelogram ABCD.
B
76. AB, AC, and mA are sufficient to solve the
triangle using the Law of Sines.
C
(A) True
5
(B) False
77. AB, AC, and mB are sufficient to solve the
triangle using the Law of Sines.
(A) True
(B) False
78. AB, AC, and BC are sufficient to solve the
triangle using the Law of Sines.

60°
A
3
D
What is the parallelogram’s area?
(A) 7.5 3
(B) 15
(A) True
(C) 15 3
(B) False
(D) 30 3
84. cos k   cos 180  k  
80. In the diagram, ABC is a non-right triangle.
C
(A) True
B
c
Which describes the area of the triangle?
(A)
(B) False
b
a
1
ab
2
(B) ab sin C
1
(C) ab sin C
2
1
(D) ab cos C
2
81. Given: cos 26  0.90 and sin 26  0.44
A
85. Let cos A  m . What is the value of sin A ?
(B) 1 – m
(C)
1  m2
(D)
1 m
86. In ABC , C is a right angle, sin A 
What is cos B?
(A)
7
4
(B)
7
3
What is the approximate value of cos 154 ?
(A) –0.90
(B) –0.44
(C) 0.44
(D) 0.90
For questions 82-84, use the statement below.
Given: An angle measures k°, where k > 0.
82. sin k   cos  90  k  
(A) True
(B) False
83. sin k   sin 180  k  
(A) True
(B) False
m
(A)
(C)
(D)
3
4
3
7
7
.
4
87. Use the diagram.
89. Use the diagram.
B
13
5
d
45°
C
A
12
What is the value of d ?
Which statement is true?
(A) sin A 
(A) 5
13
5
(B) 5 2
(C) 10
12
(B) cos A 
13
(C) tan A 
(D) 10 2
For questions 90-92, let cos x  m .
12
5
90. cos 180  x   = m
(A) True
(B) False
88. Use the diagram.
B
A
35°
x
Which is the value of x?
(A) x  41cos35
(B) x 
tan 35
41
(C) x 
41
cos 35
(D) x 
41
tan 35
91. cos  90  x   = m
41
(A) True
C
(B) False
92. sin  90  x   = m
(A) True
(B) False
93. Let a  cos28 . Which statement is true?
96. What is tan 60°?
(A) a  cos 62
(A)
2
2
(D) a  sin 152
(B)
3
2
 3
94. What is cos 1 
 ?
2


(C)
1
3
(D)
3
(B) a  cos 152
(C) a  sin 62
(A) 30°
97. What is tan 1 1 ?
(B) 45°
(C) 60°
(A) 30°
(D) 90°
(B) 45°
95. In the diagram, BC < BD and BD = AD.
(C) 60°
(D) 90°
C
1
.
2
GH I  is a dilation of GHI about G with a
scale factor of 2. What is the sine of angle G'
?
98. In GHI , the sine of angle G equals
A
B
D
(A)
1
4
(B)
1
2
Which statement is true?
(A) cos ABC  sin DAB
(B) cos ABC  sin DAB
(C) cos ABC  sin DAB
(C)
(D) 1
3
2