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2015-2016 SEMESTER EXAMS
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SEMESTER 1
For questions 1-4, use the diagram where B is the reflection of A across PQ .
1. (1.5) PA = PB
(A)
True
(B)
False
P
2. (1.7) PQ  AB
(A)
True
(B)
False
A
Q
B
3. (1.5) AQ = QB
(A)
True
(B)
False
4. (1.5) PQ 
1
AB
2
(A)
True
(B)
False
5. (2.2) 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 question 6, determine the truth of the statements about rotations.
6. (2.2) Under a rotation, no point can map to itself.
(A)
True
(B)
False
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7. (2.3) 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 8-11, determine if the described transformation(s) is/are an isometry.
8. (2.3) A reflection is an isometry.
(A)
True
(B)
False
9. (2.3) A composition of two reflections is an isometry.
(A)
True
(B)
False
10. (2.3) A dilation is an isometry.
(A)
True
(B)
False
11. (2.3) A composition of a rotation and a dilation is an isometry.
(A)
True
(B)
False
For question 12, a transformation S is defined as (𝑥, 𝑦) → (3𝑥, 𝑦 − 1).
12. (2.3) S is an isometry.
(A)
True
(B)
False
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For questions 13-16, determine if the mapping is an isometry.
13. (2.3) (𝑥, 𝑦) → (𝑥, 𝑦 + 2) is an isometry.
(A)
True
(B)
False
14. (2.3) (𝑥, 𝑦) → (−𝑥, 𝑦) is an isometry.
(A)
True
(B)
False
15. (2.3) (𝑥, 𝑦) → (𝑦, 𝑥) is an isometry.
(A)
True
(B)
False
16. (2.3) (𝑥, 𝑦) → (2𝑥, 𝑦) is an isometry.
(A)
True
(B)
False
17. (2.4) Which transformation does NOT preserve the orientation of a figure?
(A)
dilation
(B)
reflection
(C)
rotation
(D)
translation
For question 18, determine the truth of the statements about rotations.
18. (2.4) Rotations preserve the orientation of a figure.
(A)
True
(B)
False
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19. (2.4) Use the figure.
A transformation T is defined as (𝑥, 𝑦) → (𝑥, −𝑦).
Which shows the image of figure under T?
(A)
(B)
(C)
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For question 20-21, point P is located at (6, 0) and undergoes a transformation.
20. (2. 4) A rotation of 90° about P results in P = P.
(A)
True
(B)
False
21. (2.4) A translation by the vector ⟨−6, 0 ⟩ results in P = P.
(A)
True
(B)
False
y

22. (2.4) Use the figure.
A
(a) Transform ABC by reflecting it
across the y-axis to produce ABC .
(b) Describe a transformation, or
composition of transformations, that
maps ABC to DEF .
B
C

F
E
D
 x
(c) Describe a single transformation
that maps ABC to DEF .

23. ( 2.4) ABC is the image of ABC when a
reflected about line .
A'
B'
A
B
C'
C
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24. (2.5) What is the image of the point (–4, 6) under the transformation ?
(A)
(6, 4)
(B)
(–6, –4)
(C)
(4, 6)
(D)
(–4, –6)
25. (2.5) 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
(B)
 x, y     x  4,  y 1
(C)
 x, y     y  4, x  1
(D)
 x, y     y  4, x  1
For question 26, a transformation S is defined as  x, y    3x, y  1 .
26. (2.5) The pre-image of A  3, 6  under S is A 9, 5 .
(A)
True
(B)
False
27. (2.5) 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)
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28. (2.5) A reflection about the x axis results in P = P.
(A)
True
(B)
False
29. (2.6) 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.
O
30. (2.6) Draw the image of ABC when rotated 70° about O.
A
B
C
31. (2.6) ABC is the image of ABC when rotated about point O. Construct point O
and compute the angle of rotation.
A
C'
B
B'
C
A'
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32. (2.7) The point A(4, 3) is rotated –90° about the origin. In which quadrant is A' ?
(A)
I
(B)
II
(C)
III
(D)
IV
m
33. (2.7) Use the diagram.

k
Which series of reflections would result in a rotation of –44°
about A?
(A)
reflect across k¸ then reflect across 
(B)
reflect across ¸ then reflect across k
(C)
reflect across ¸ then reflect across m
(D)
reflect across m¸ then reflect across 
44°
22°
A
34. (2.7) 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
35. (2.7) 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
(B)
a reflection across the line y = 6
(C)
a translation 2 units up
(D)
a translation 4 units up
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36. (2.7) In the diagram, 𝑔 ∥ 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
37. (2.7) 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
38. (2.7) Draw the image of ABC when reflected
across line m.
For questions 39-40, use the diagram which shows
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A
m
B
C
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SEMESTER 1
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
C
A

39. (2.7) The equation of line  is x = –0.5.
(A)
True
(B)
False
40. (2.7) 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
41. (2.8) 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
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42. (2.7) Jimmy is building a go-cart to race. Jimmy sits in a seat toward the left rear
corner of the cart. To see other carts behind him, he mounts 3 plane mirrors: one on
each side of the cart and one in the center.
The scale diagram shows a top view of the cart.
Front of Cart
center mirror
left side mirror
right side mirror
J
1 foot
Seat
(a) Jimmy’s eyes are at point J. The mirrors are mounted in a way that Jimmy
does not block his own view. Show the area behind the cart that Jimmy can
see using the mirrors.
(b) Describe how Jimmy could improve his visibility behind the cart using the
same three mirrors.
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For questions 43-45, use the diagram showing parallelogram ABCD.
A
E
B
I
H
D
F
G
C
43. (2.8) A reflection across EG carries parallelogram ABCD onto itself.
(A)
True
(B)
False
44. (2.8) A rotation of 90° about I carries parallelogram ABCD onto itself.
(A)
True
(B)
False
45. (2.8) A rotation of 180° about I carries parallelogram ABCD onto itself.
(A)
True
(B)
False
For questions 46-48, evaluate whether the image of a figure under the described
transformation is congruent to the figure.
46. (2.8) A transformation T follows the rule  x, y    x  3, y  . The image of a figure
under T is congruent to the figure.
(A)
True
(B)
False
47. (2.8) A transformation T follows the rule  x, y     y,  x  . The image of a figure
under T is congruent to the figure.
(A)
True
(B)
False
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48. (2.8) A transformation T follows the rule  x, y    x, 2 y  . The image of a figure
under T is congruent to the figure.
(A)
True
(B)
False
49. (2.8) 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
50. (2.8) The diagram shows regular hexagon ABCDEF with center O. For each part, fill
in the blank.
A
F
(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
_____.
B
E
O
(c) F is the image of D when the figure is rotated _____° about O.
(d) B is first reflected across FC . That image maps to F when
reflected across _____.
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C
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D
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51. (4.3) Use the diagram.
(A)
1 and 3 are congruent
(B)
2 and 7 are complementary
(C)
4 and 1 are congruent
(D)
8 and 6 are supplementary
s
r
Which statement would be used to prove lines r
and s are parallel?
m
3 4
1 2
n
8 7
6 5
52. (4.3) In the diagram, 𝑚 ∥ 𝑛 𝑎𝑛𝑑 𝑝 ∥ 𝑞.
p
What is the value of x?
(A)
44
(B)
88
(C)
92
(D)
176
q
m
88°
n
x°
53. (5.1) In ABC , M is the midpoint of AB and N is the midpoint of AC . For which
1
type of triangle is MN  BC ?
2
(A)
equilateral only
(B)
isosceles only
(C)
scalene only
(D)
any triangle
For questions 54-55, consider ABC where AB = BC and mA  40 .
54. (5.2) mB  mC  140
(A)
True
(B)
False
55. (5.2) mC  100
(A)
True
(B)
False
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SEMESTER 1
56. (5.2) Prove the sum of the measures of the interior angles of any triangle is 180°.
57. (5.5) On the coordinate plane, draw triangles ABC and ABC such that:
(1) A = A
(2) ABC has been rotated 90°.
For questions 58-60, 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.
58. (5.6)
Given
Conclusion
A  X
B  Y
ABC  XYZ
C  Z
(A)
True
(B)
False
59. (5.6)
Given
Conclusion
A  X
B  Y
ABC  XYZ
BC  YZ
(A)
True
(B)
False
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60. (5.6)
Given
A   X
Conclusion
AB  XY
ABC  XYZ
BC  YZ
(A)
True
(B)
False
61. (5.6) In the diagram, m is the perpendicular bisector of AB at C, and rm  D   E .
m
E
D
A
C
B
Prove ADC  BEC .
62. (5.6) In the diagram, DC is the perpendicular bisector of AB .
D
Prove DAB  DBA .
A
C
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B
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B
63. (5.6) Use the diagram.
Given:
Prove:
E
BD  AC
AE  BC
F
∆𝐴𝐸𝐶 ≅ ∆𝐵𝐷𝐶
A
C
D
For questions 64-66, use the diagram where ABCD is a quadrilateral with ̅̅̅̅
𝐴𝐵 ∥ ̅̅̅̅
𝐶𝐷 and
̅̅̅̅ ∥ 𝐵𝐶
̅̅̅̅ . Diagonals 𝐴𝐶
̅̅̅̅ and 𝐵𝐷
̅̅̅̅ intersect at E.
𝐴𝐷
B
A
E
C
D
64. (6.3) CBE  ABE
(A)
True
(B)
False
65. (6.3) ADE  ABE
(A)
True
(B)
False
66. (6.3) CDE  ABE
(A)
True
(B)
False
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67. (6.3) Which of the following is not a characteristic of all parallelograms?
(A) Consecutive angles are supplementary
(B) Opposite angles are congruent
(C) Diagonals bisect each other
(D) Diagonals are angle bisectors
68. (6.6) Which of the following is not a characteristic of all rectangles?
(E) Consecutive angles are supplementary
(F) Diagonals are perpendicular
(G) Diagonals bisect each other
(H) Opposite angles are congruent
69. (6.6) Given rectangle NOPQ , if the mPNO  23 then the mPNQ is:
(I) 23
O
N
(J) 46
Z
(K) 67
(L) 75
P
Q
70. (6.6) Given rhombus EFGH , if the mFGE  25 then the mEFG is:
(M) 65
F
G
(N) 115
(O) 130
X
E
(P) 155
H
71. (6.6) If you rotate RST 180 about point U, the most specific name for the resulting
quadrilateral is:
S
(Q) Parallelogram
U
(R) Rhombus
(S) Rectangle
R
(T) Trapezoid
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o
V
x
T
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72. (6.6) Use scalene right triangle ABC.
Describe and sketch the transformations required so
that the union of the triangle and its image forms
(a)
a kite.
(b)
an isosceles triangle.
(c)
a rectangle.
B
C
A
73. (6.6) Use the Venn diagram.
Quadrilateral
sI
Rhombi
Parallelogram
s
Squares
Rectangles
III
IV
V
II
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
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