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Name: ____________________________________________
CC Geometry

Unit 2 Test Review

Transformations, Rigid Motions and Congruence

1) Which figure does not have line symmetry? 5) Refer to the diagram below.

A)

B)

C)

D)

What two transformations took triangle ABC to

triangle A2B2C2?
A) a rotation of 180D about the origin
followed by a translation of (-2,-3)
2) What is the image of A(3,4) under R90D? B) a translation of (1,-2) followed by a
reflection over the x-axis
A) (-4,3) C) (-4,-3) C) a translation of (1,-3) followed by a
B) (-3,-4) D) (3,-4) rotation of 180D about point A
D) a reflection over the x-axis followed by a
translation of (1,-2)
3) What is the image of the point (-3,-1) under the
translation that shifts (x,y) to (x - 2,y + 4)?
A) (-1,-5) C) (-5,-5) 6) Which figure has 60D rotational symmetry?
B) (-5,3) D) (-1,3)
A) regular hexagon
B) square
C) equilateral triangle
D) regular octagon
4) Which rotation about the origin is equivalent to
R-200D?
A) R-160D C) R160D
B) R200D D) R560D
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7) Which letter has point symmetry? 10) In the diagram below, hA1B1C1 is a
A) C) transformation of hABC, and hA2B2C2 is a
transformation of hA1B1C1.
B) D)

8) In the accompanying diagram, hA1B1C1 is the

image of hABC.

The composite transformation of hABC to

Which type of transformation is shown in the hA2B2C2 is an example of a
illustration? A) translation followed by a reflection
A) dilation B) reflection followed by a rotation
B) rotation C) reflection followed by a translation
C) line reflection D) translation followed by a rotation
D) translation

11) Which figure has 120D rotational symmetry?

9) If hJKL C hMNO, which statement is always A) rhombus
true? B) equilateral triangle
A) AKJL C AMON C) regular pentagon
B) JK C ON D) square
C) AKLJ C ANMO
D) JL C MO

12) The image of A(-1,3) under the translation T2,1

is
A) (-3,2) C) (1,4)
B) (0,5) D) (-2,3)
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13) The rectangle ABCD shown in the diagram below will be reflected across the x-axis.

What will not be preserved?

A) measure of AA C) length of AB
B) parallelism of AB and CD D) slope of AB

14) In the diagram below, hABC C hXYZ. 15) Which figures have both point symmetry and
line symmetry?

A) none of the figures

B) B and C, only
Which two statements identify corresponding C) all of the figures
congruent parts for these triangles? D) A and C, only
A) BC C YZ and AA C AX
B) AB C XY and AC C AY
C) AB C YZ and AC C AX
16) Pentagon PQRST has PQ parallel to TS. After a
D) BC C XY and AA C AY
translation of T2,-5, which line segment is
parallel to P1Q1?
A) T1S1 C) T1P1
B) R1S1 D) R1Q1
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17) Which polygon has rotational symmetry of 90D? 20) A regular hexagon is rotated in a
A) regular pentagon counterclockwise direction about its center.
B) equilateral triangle Determine and state the minimum number of
degrees in the rotation such that the hexagon
C) regular hexagon
will coincide with itself. [Show all work.]
D) square

18) Under a translation, the image of point (3,2) is

(-1,3). What are the coordinates of the image of
point (-2,6) under the same translation?

21) In the diagram below, hABC and hXYZ are

graphed.

19) After a reflection over a line, hA1B1C1 is the

image of hABC. Explain why triangle ABC is
congruent to triangle A1B1C1.

Use the properties of rigid motions to explain

why hABC C hXYZ.
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22) In the accompanying diagram, AC and DE bisect each other at B.

Prove that hABD C hCBE using transformation geometry axioms and isometry properties.

23) Triangle TAP has coordinates T(-1,4), A(2,4), and P(2,0).

On the set of axes below, graph and label h T1A1P1, the image of hTAP after the translation
(x,y) ‚ (x * 5,y * 1).
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24) Triangle XYZ, shown in the diagram below, is reflected over the line x = 2. State the coordinates of
hX1Y1Z1, the image of hXYZ.

25) The grid below shows hABC and hDEF.

(a) Let hA1B1C1 be the image of hABC after a rotation about point A. Determine and state the location
of B1 if the location of point C1 is (8,3). [Explain your answer.]

(b) Is hDEF congruent to hA1B1C1? [Explain your answer.]

 Answer Key 5938 - 1 - Page 1
1) C 2) A 3) B 4) C 5) D

6) A 7) B 8) C 9) D 10) A

11) B 12) C 13) D 14) A 15) D

16) A 17) D

18) (-6,7)

19) SAMPLE EXPLANATION: Reflections are rigid motions, and during rigid motions, distances remain the same. So, AB C A1B1
and BC C B1C1 and AC C A1C1. The triangles are congruent by SSS.

20) 60D
WORK SHOWN: = 60

21) SAMPLE EXPLANATION: hXYZ is the image of hABC after a rotation of 180D about the origin. In any rotation, distance is
preserved because rotation is a rigid motion. Thus, the triangles are congruent.

22) Answer is a proof.

23)

24) X1(5,1), Y1(4,4), and Z1(7,4)

WORK SHOWN:

25) (a) B1(7,1)

 Answer Key 5938 - 1 - Page 2
SAMPLE EXPLANATION: The angle of rotation that took C to C1 was 90D counter-clockwise. So the angle of rotation that
takes B to B1 is also 90D. The slope of AB = * . The slope of AB1 (the line perpendicular to AB) = . So the coordinate of
B1 is (5 + 2,4 * 3) = (7,1);
(b) Yes
SAMPLE EXPLANATION: When hA1B1C1 is reflected over the line x = -1, it will map the hDEF. Since a reflection is a
rigid motion, distance is preserved. Therefore, hDEF C hA1B1C1 by SSS.