Name: ________________________ Class: ___________________ Date: __________
Unit 2 Congruency Assessment
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
ABC 
1.
a.
b.
____
5
14
c.
d.
10
9
2. What single rigid motion can move the solid figure onto the dashed figure?
a.
b.
____
DEF . What is the value of x ?
reflection
dilation
c.
d.
rotation
translation
3. If the two triangles are congruent, what is the length of x?
a.
b.
12
16
c.
d.
1
14
28
ID: B
Name: ________________________
____
ID: B
4. Prove that the triangles with the given vertices are congruent.
A(3, 1), B(4, 5), C(2, 3)
D(–1, –3), E(–5, –4), F(–3, –2)
a. The triangles are congruent because ABC can be mapped onto DEF
(x,y)  (y,x), followed by a reflection: (x,y)  (x,y).
b. The triangles are congruent because ABC can be mapped onto DEF
(x,y)  (y,x), followed by a reflection: (x,y)  (x,y).
c. The triangles are congruent because ABC can be mapped onto DEF
(x,y)  (x  4,y), followed by another translation: (x,y)  (x,y  6).
d. The triangles are congruent because ABC can be mapped onto DEF
(x,y)  (x,y), followed by a rotation: (x,y)  (y,x).
by a rotation:
by a rotation:
by a translation:
by a reflection:
____
5. The transformation:  x, y    x  5, y  7  is a __________.
a. Dilation
b. Rotation
c. Translation
d. Reflection
____
6. Obtuse triangle ABC  obtuse triangle DEF. mA = 104 and mF = 32. Find mB.
a. 32
c. 44
b. 104
d. 42
____
7. Write a congruence statement for the pair of congruent polygons.
a.
b.
c.
d.
Triangle FGH  triangle JKL
Triangle FGH  triangle KLJ
Triangle FGH  triangle LJK
Triangle HFG is congruent to triangle KLJ.
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Name: ________________________
____
8. Are rectangles ABCD and WXYZ congruent? If so, what is a sequence of transformations that maps ABCD to
WXYZ ?
a.
b.
c.
d.
____
ID: B
Yes; reflect across the y-axis and then rotate 90 counterclockwise about the origin.
No; there is no sequence of transformations that maps ABCD to WXYZ.
Yes; rotate 90 clockwise about the origin and then translate 8 units left.
Yes; reflect across the x-axis and then translate 8 units left.
9. Determine whether triangles
a.
b.
c.
d.
EFG and
The triangles are congruent because
(x,y)  (x,y).
The triangles are congruent because
(x,y)  (y,x).
The triangles are congruent because
(x,y)  (x,y).
The triangles are congruent because
(x,y)  (y,x).
PQR are congruent.
EFG can be mapped to
PQR by a reflection:
EFG can be mapped to
PQR by a rotation:
EFG can be mapped to
PQR by a reflection:
EFG can be mapped to
PQR by a rotation:
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Name: ________________________
ID: B
____ 10. Which of the following is not a congruence transformation?
a. A dilation with scale factor 0.5.
b. A dilation with scale factor 1.
c. A reflection over the x-axis.
d. A translation 1 unit left.
____ 11. Given AB  DE , B  E , and BC  EF , which is a good first step when proving that
a.
b.
c.
d.
Find a sequence of rigid motions that maps AB onto BC .
Find a sequence of rigid motions that maps A onto F .
Find a sequence of rigid motions that maps AB onto DE .
Translate ABC so it maps onto DEF .
____ 12. Which describes the transformation from the original to the image, and tells whether the
two figures are similar or congruent?
a.
b.
rotation, congruent
rotation, similar
c.
d.
4
dilation, similar
translation, congruent
ABC 
DEF ?
Name: ________________________
ID: B
____ 13. Which describes the transformation from the original to the image, and tells whether the
two figures are similar or congruent?
a.
b.
reflection, congruent
translation, congruent
c.
d.
translation, similar
dilation, similar
____ 14. A figure lies in Quadrant II of a coordinate plane. The figure is transformed by first reflecting across the
x-axis and then rotating 90 clockwise about the origin. In what quadrant will the image lie?
a.
b.
c.
d.
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
5
Name: ________________________
ID: B
____ 15. What is the best first step when finding a sequence of rigid motions to map
a.
b.
c.
d.
____ 16. If
a.
b.
c.
d.
____ 17. If
a.
b.
c.
d.
ABC to
DEF ?
Find a single transformation that maps one vertex of ABC to the corresponding vertex
of EFD.
Find a single transformation that maps one vertex of ABC to the corresponding vertex
of DEF .
Find a single transformation that maps one side of ABC to the corresponding side of
DEF .
Find a single transformation that maps one angle of ABC to the corresponding angle of
another triangle AB C .
ABC 
GHI , what is the length of GH ?
10
23
13
The length cannot be determined.
ABC 
DEF , which segment is congruent to AC ?
EF
AB
DE
DF
6
Name: ________________________
ID: B
____ 18. Which sequence of transformations shows that figures A and B are congruent?
a.
b.
c.
d.
Reflect figure A across the x-axis and then translate right 6 units and up 1 unit.
Reflect figure A across the y-axis and then translate right 1 unit and up 4 units.
Rotate figure A 90 clockwise about the origin and then translate right 5 units.
Rotate figure A 90 counterclockwise about the origin and then translate down 5 units.
____ 19. For two triangles with identical orientation, what rigid motion is necessary for SAS congruence to be shown?
a.
b.
Rotation
Dilation
c.
d.
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Reflection
Translation
Name: ________________________
ID: B
____ 20. Figure A is congruent to figure B. What sequence of transformations maps figure A to figure B?
a.
b.
c.
d.
(x, y)  (x, y) followed by (x, y)  (x, y  2)
(x, y)  (x,  y) followed by (x, y)  (x, y  2)
(x, y)  (x, y  2) followed by (x, y)  (x,  y)
(x, y)  (x, y  2) followed by (x, y)  (x, y)
____ 21. What information is needed to prove
a.
b.
KL  9.5
KM  9.5
MLK 
PQR by SAS?
c.
d.
KL  10
KM  10
____ 22. Describe the transformation M:  x, y    x,  y  .
a. A reflection across the x-axis.
b. A translation one unit down and one unit to the right.
c. A rotation 180 with center of rotation  0, 0  .
d. A dilation with a scale factor 1 and center  0, 0  .
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