Semester 1 Exam Review
Regular Geometry
Name_________________________________________
1. What term describes a transformation that does not change a figure’s size or shape?
(A)
similarity
(B) isometry
(C) collinearity
(D) symmetry
For questions 2–4, use the diagram showing parallelogram ABCD.
A
E
B
I
H
D
F
G
C
2. True or False. A reflection across EG carries parallelogram ABCD onto itself.
3. True or False. A rotation of 90° about I carries parallelogram ABCD onto itself.
4. True or False. A rotation of 180° about I carries parallelogram ABCD onto itself.
5. Which of these is equivalent to a translation?
(A) a reflection across one line
(B) a composition of two reflections across intersecting lines
(C) a composition of two reflections across parallel lines
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°.
Which could NOT be the value of n?
(A) 3
(B) 4
(C) 5
(D) 6
7. What is the image of the point (–4, 6) under the transformation T  x, y     y, x  ?
(A) (6, 4)
(B)
(–6, –4)
(C)
(4, 6)
(D)
(–4, –6)
8. In the diagram, g ll h and B lies on line g.
10 cm
5 cm
B
C
A
g
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
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?
(A)
 x, y    x  4,  y  1
(C)
 x, y     y  4, x  1
(B)
 x, y     x  4,  y 1
(D)
 x, y     y  4, x  1
10. The point A(4, 3) is rotated –90° about the origin. In which quadrant is A' ?
(A) I
(B) II
(C) III
(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?
(A) a reflection across the line y = 3
(C) a translation 2 units up
(B) a reflection across the line y = 6
(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?
(A) a reflection across 
(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
For questions 13–16, determine if the described transformation(s) is/are an isometry.
13.
True or False. A reflection is an isometry.
14.
True or False. A composition of two reflections is an isometry.
15.
True or False. A dilation is an isometry.
16.
True or False. A composition of a rotation and a dilation is an isometry.
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
(D) any triangle
18. Use the diagram.
m
Which series of reflections would result in a
rotation of –44° about A?

k
(A) reflect across k¸ then reflect across 
44°
22°
(B) reflect across ¸ then reflect across k
(C) reflect across ¸ then reflect across m
A
(D) reflect across m¸ then reflect across 
19. After a figure is rotated, P  P . Which statement(s) could be true?
(A) The center of rotation is P.
(C) Either A or B or both.
(B) The angle of rotation is a multiple of 360°.
(D)
Neither A nor B.
For questions 20–23, use the diagram where B is the reflection of A across ⃡𝑷𝑸.
P
Q
A
B
20. True or False. PA = PB
21. True or False. PQ  AB
22. True or False. AQ = QB
1
2
23. True or False. PQ  AB
For questions 24–26, use the diagram where ABCD is a quadrilateral with
𝑨𝑩 || 𝑫𝑪 and 𝑩𝑪 || 𝑨𝑫. Diagonals AC and BD intersect at E.
B
A
E
C
D
24. True or False. CBE  ABE
25. True or False. ADE  ABE
26. True or False. CDE  ABE
For questions 27–28, a transformation S is defined as  x, y    3x, y  1 .
27. True or False. The pre-image of A  3, 6  under S is A 9, 5 .
28. True or False. S is an isometry.
29. Use the figure.
A transformation T is defined as  x, y    x, – y  . Which shows the image of figure under T?
(A)
(B)
(C)
30. Given point A is located at (1, 3). What is the final image of A after this series of
transformations?
(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)
(C) (–3, –1)
(D) (–5, 5)
31. Which transformation does NOT preserve the orientation of a figure?
(A) dilation
(B) reflection
(C) rotation
(D) translation
For questions 32–35, determine if the mapping is an isometry.
32. True or False.
 x, y    x, y  2 is an isometry.
33. True or False.
 x, y    x, y  is an isometry.
34. True or False.
 x, y    y, x 
35. True or False.
 x, y    2x, y 
is an isometry.
is an isometry.
36. 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) rotation
(D) translation
For questions 37–38, determine the truth of the statements about rotations.
37. True or False. Rotations preserve the orientation of a figure.
38. True or False. Under a rotation, no point can map to itself.
For questions 39–41, point P is located at (6, 0) and undergoes a transformation.
39. True or False. A rotation of 90° about P results in P = P.
40. True or False. A translation by the vector 6, 0 results in P = P.
41. True or False. A reflection about the x axis results in P = P.
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

B
B

m
 x
A
C

42. True or False. The equation of line  is x = –0.5.
43. True or False. 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.
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
ABC  XYZ
(A) True
(B) False
C  Z
45.
Given
A  X
Conclusion
B  Y
ABC  XYZ
(A) True
(B) False
BC  YZ
46.
Given
A   X
Conclusion
AB  XY
ABC  XYZ
BC  YZ
(A) True
(B) False
47. Look at the figure below.
Look at these three figures.
II
III
I
Which figures are congruent to the first figure?
(A) I only
(B)
II only
(C) I and II only
(D)
I, II, and III
48. Use the diagram.
s
r
m
3 4
1 2
n
8 7
6 5
Which statement would be used to prove lines r and s are parallel?
(A) 1 and 3 are congruent
(C) 4 and 1 are congruent
(B) 2 and 7 are complementary
(D) 8 and 6 are supplementary
For questions 49–51, evaluate whether the image of a figure under the described
transformation is congruent to the figure.
49. True or False. A transformation T follows the rule  x, y    x  3, y  . The image of a figure
under T is congruent to the figure.
50. True or False. A transformation T follows the rule  x, y     y,  x  . The image of a figure
under T is congruent to the figure.
51. True or False. A transformation T follows the rule  x, y    x, 2 y  . The image of a figure
under T is congruent to the figure.
52. In the diagram, m || n and w || s.
w
What is the value of x?
(A) 44
(C) 92
(B)
(D) 176
88
s
m
88°
n
x°
For questions 53–54, consider ABC where AB = BC and mA  40 .
53. True or False. mB  mC  140
54. True or False. mC  100
55. Use the Venn diagram.
Quadrilaterals
I
Parallelograms
II
Rhombi
Squares
Rectangles
III
IV
V
Trapezoids
VI
VII
Kites
A quadrilateral ABCD has 4 lines of symmetry. Identify the area of the diagram in which
ABCD resides.
(A) III
(B) IV
(C) V
(D) VII
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'?
(A) 96 square units
(C) 384 square units
(B) 192 square units
(D) 768 square units
57. In the diagram below 𝑩𝑪 || 𝑫𝑯.
A
What is the value of y?
4
(A) 13
9
H
D
(B) 18
y
8
(C) 27
B
C
58. 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?
(A) 3.0 cm
(C) 13.0 cm
(B) 10.7 cm
(D) 21.3 cm
59. 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.
What is the height of the tree?
(A) 24 m
(B) 35 m
(C) 41 m
(D) 59 m
2m
3m
36 m
60. In the diagram, 𝑱𝑮 || 𝑸𝑹.
What is the value of x?
Q
J
(A) 11
(B) 6
7
(C) 5
(D) 3
R
P
4
x
G
8
61. Which figure contains two similar triangles that are NOT congruent?
(A)
(C)
(B)
(D)
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.
(B) The triangles could be similar.
(C) The triangles must be similar.
63. Triangle ABC has vertices A 2, 2  , B  5, 5 , and C  5, 3 . The triangle is 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
64. Dilate line m about the origin with scale factor 2. What is the equation of the line’s image?
What is the value of x?
(A) y = 2x + 2
(B)
y = 2x + 4
(C) y = 4x + 2
(D) y = 4x + 4
m
65. Which is NOT a criterion for triangle similarity?
(A) angle-angle
(B) angle-side-angle
(D) side-side
1
about P. Which shows the result of the dilation?
2
66. Dilate line m by a factor
y
(C) side-angle-side
Choice A
Choice B
Choice C
Choice D
y
y
y
y
m
x
m’
m’
P
m’
m’
x
x
P
P
P
67. In the diagram, segments AB and CD intersect at E, F lies on AB , and mAEC  60 .
D
B
F
E
A
60°
C
The two segments are dilated about F with scale factor
(A) 30°
(B)
60°
(C)
90°
1
. What is mAEC ?
2
(D)
120°
For questions 68–70, use the diagram. Let the figure be dilated with scale factor k,
where k  0 and k  1.
68. True or False. mABE  k  mABE  .
E
69. True or False. G' is between B' and F'.
70. True or False. CD  k  CD 
x
x
D
C
A
B
G
F
P
1
71. In the diagram, ABCD is dilated with center O to produce A'B'C'D', and AB  AB
3
A
A'
F
D
D'
O
C'
B'
C
B
What is
(A)
1
3
OA
?
AA
(B)
1
(C)
2
2
(D)
72. Use the figure below.
Which shows the figure dilated about the origin with scale factor 1.5?
A)
B)
C)
3
73. One vertex of a polygon is A(–4, 5). If the polygon is dilated about the point (0, 2) with scale
factor –2, what is the location of A?
(A) (–8, 8)
(B) (–8, 10)
(C) (8, –10)
(D) (8, –4)
74. J(5, 7) is the image of J(3, 3) after a dilation with factor 3. Where is the center of dilation?
(A) (–3, –9)
(B) (0, 0)
(C) (2, 1)
(D) (4, 5)
75. Fred stands at corner A of a rectangular field shown below. He needs to get to corner C.
What is the shortest distance from A to C?
(A)
9m
(B)
13 𝑚
A
9m
(C) 15 m
D
(D) 21 m
76. Use the right triangle. What is the value of x?
(A)
7
(B)
√161
15
x
(C) 7
(D) 17
B
8
12 m
C
77. Use the diagram.
Which is equal to h?
(A)
ay
(B)
bx
(C)
xy
(D)
ab
C
b
a
h
x
y
A
B
D
c
If an angle measures k°, where k > 0, then sin k   cos  90  k  
78. True or False.
79. Let cos A  m . What is the value of sin A ?
(A)
m
(B)
1–m
(C)
√1 − 𝑚2
80. In ABC where C is a right angle, sin A 
(A)
81.
7
4
(B)
7
3
(C)
3
4
(D) √1 − 𝑚
7
. What is cos B?
4
(D)
3
7
Use the diagram.
Which statement is true?
B
(A) sin A =
(B) cos A =
(C) tan A =
13
5
12
5
13
13
12
5
C
12
A
82. Use the diagram.
Which statement is true?
(A) x = 41cos35°
(B)
x=
B
(C) x =
tan 35°
(D)
41
x=
41
41
cos 35°
35°
A
41
C
x
tan 35°
83. Use the diagram.
What is the value of d?
(A)
5
(B) 5√2
(C) 10
(D)
5 2
10√2
d
45°
For questions 84 - 85, let cos x  m .
84. True or False. cos  90  x   = m
85. True or False. sin  90  x   = m
86. Let a  cos28 . Which statement is true?
(A) a  cos 62
(B) a = cos 152°
(C) a = sin 62°
(D) a = sin 152°
 3
87. What is cos 1 
 ?
2


(A) 30°
(B)
45°
(C)
60°
(D) 90°
88. In the diagram, BC < BD and BD = AD.
C
(A)
cos∠ABC < sin ∠ DAB
A
(B) cos∠ABC = sin ∠ DAB
B
(C) cos∠ABC > sin ∠ DAB
D
89. What is tan 60°?
(A)
2
2
(B)
√3
2
1
(C)
√3
(D) √3
90. What is tan 1 1 ?
(A) 30°
(B) 45°
(C) 60°
(D) 90°
1
. GH I  is a dilation of GHI about G with a scale
2
factor of 2. What is the sine of angle G' ?
91. In GHI , the sine of angle G equals
(A)
91b.
1
4
(B)
1
2
(C)
√3
2
(D) 1
Which of the following is not a characteristic of all parallelograms?
(A)
Consecutive angles are supplementary
(C) Diagonals bisect each other
(B)
Opposite angles are congruent
(D) Diagonals are angle bisectors.
92. Which of the following is not a characteristic of all rectangles?
(A) Consecutive angles are supplementary
(B) Diagonals are perpendicular
(C) Diagonals bisect each other
(D) Opposite angles are congruent
93. Given rectangle NOPQ , if the mPNO  23 then the mPNQ is:
(A) 23
O
N
(B) 46
(C) 67
Z
(D) 75
P
Q
94. Given rhombus EFGH , if the mFGE  25 then the mEFG is:
(A) 65
F
G
(B) 115
X
(C) 130
E
(D) 155
H
95. If you rotate ΔRST 180 about point U, the most specific name for the resulting quadrilateral
is:
S
(A) Parallelogram
U
(B) Rhombus
(C) Rectangle
R
o
V
x
(D) Trapezoid
T
96. The diagram shows regular hexagon ABCDEF with center O.
A
B
F
O
C
E
D
For each part, fill in the blank.
(a) _____ is the image of A under a 60° rotation about O.
(b) The figure is reflected across AD . The pre-image of E is _____.
(c) F is the image of D when the figure is rotated _____° or _____°about O.
(d) B is first reflected across FC . That image maps to F when reflected across _____.