Download 2nd Nine Weeks Extra Credit ID B

Name: ________________________ Class: ___________________ Date: __________
2nd Nine Weeks Extra Credit (Unit 2)
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. If
a.
b.
c.
d.
____
DEF , which segment is congruent to AC ?
DF
AB
EF
DE
2. Triangle ABC is similar to triangle DEF. What is the value of x ?
a.
b.
____
ABC 
20
15
c.
d.
30
60
3. In the figure, quadrilateral RSTU  quadrilateral HIFG. Find b.
a.
b.
b = 75
b=5
c.
d.
1
b = 98
b = 70
ID: B
Name: ________________________
____
ID: B
4. Which describes the transformation from the original to the image, and tells whether the
two figures are similar or congruent?
a.
b.
dilation, similar
rotation, congruent
c.
d.
translation, congruent
rotation, similar
____
5. Translate the quadrilateral W  2,2  , X  3,3  , Y  6,5  , Z  6,3  using the transformation  x  2,y  3  .
a. W'  0,5  , X'  1,6  , Y'  4,8  , Z'  4,6 
b. W'  4,5  , X'  5,6  , Y'  8,8  , Z'  8,6 
c. W'  0, 1  , X'  1,0  , Y'  4,2  , Z'  4,0 
d. W'  4,6  , X'  6,9 , Y'  12,15  , Z'  12,9 
____
6. Describe the transformation M:  x, y    x,  y  .
a. A reflection across the x-axis.
b. A dilation with a scale factor 1 and center  0, 0  .
c. A rotation 180 with center of rotation  0, 0  .
d. A translation one unit down and one unit to the right.
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Name: ________________________
____
7. In the figure, 6 and 2 are _____________.
a.
b.
____
consecutive interior angles
corresponding angles
c.
d.
alternate exterior angles
alternate interior angles
8. At the same time of day, a man who is 76 inches tall casts a 57-inch shadow and his son casts a 24-inch
shadow. What is the height of the man's son? (Figures may not be drawn to scale.)
a.
____
ID: B
108 in.
b.
33 in.
c.
32 in.
d.
9. What is the image of  8,1  when it is reflected across the line y  x ?
 1

a.  1,8 
c.   ,1 
 8



1
b.  1,8 
d.  1, 

8 
____ 10. Which mapping represents a rotation of 270 clockwise about the origin?
a.  x,y    y, x 
c.  x,y    x,y 
b.  x,y    y,x 
d.  x,y    x, y 
3
81 in.
Name: ________________________
ID: B
____ 11. In the figure, 6 and 3 are __________.
a.
b.
corresponding angles
alternate exterior angles
c.
d.
consecutive interior angles
alternate interior angles
____ 12. A triangle has vertices (4, 1), (3, 0), and (7, 2). What are the vertices of the image of the triangle after a
reflection across the y-axis?
a. (4, 1), (3, 0), and (7, 2)
b. (1, 4), (0, 3), and (2, 7)
c. (4, 1), (3, 0), and (7, 2)
d. (4, 1), (3, 0), and (7, 2)
____ 13. The postulate or theorem that can be used to prove that the two triangles are similar is _____.
a.
b.
SSS Similarity
ASA Congruence
c.
d.
SAS Similarity
AA Similarity
____ 14. If the two triangles are congruent, what is the length of x?
a.
b.
12
14
c.
d.
4
28
16
Name: ________________________
ID: B



____ 15. Which of the following proportions could be used as a given to show that AB  DF ?
a.
b.
c.
d.
DE
DF
EF
DF
DA
AE
DA
BE
AE
AB
EB

AB
FB

BE
AE

BE

____ 16. In the figure below, A  D and B  E . To show that ABC  DEF , you can apply a dilation to
ABC so that the image is congruent to DEF . What is the scale factor of the dilation?
a.
b.
c.
d.
BC
EF
AD
BE
AB
DE
DF
AC
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Name: ________________________
ID: B
____ 17. Given a triangle with vertices A  4,  1  , B  3, 0  , and C  7, 2  , which points represent a reflection of
ABC in the y-axis?
a. A  1, 4  , B  0,  3  , C  2, 7 
c. A  4, 1  , B  3, 0  , C  7,  2 
b. A  4, 1  , B  3, 0  , C  7,  2 
d. A  4,  1  , B  3, 0  , C  7, 2 
____ 18. What information is needed to prove
a.
b.
MLK 
KM  10
KL  10
PQR by SAS?
c.
d.
KM  9.5
KL  9.5
c.
d.
AOC
COD
____ 19. Name an angle supplementary to AOE .
a.
b.
AOB
BOC
____ 20. What is the image of the point  10,6  after a 90 counterclockwise rotation?
a.  10,6
c.  6, 10 
b.  10, 6 
d.  6,10
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Name: ________________________
ID: B
____ 21. For two triangles with identical orientation, what rigid motion is necessary for SAS congruence to be shown?
a.
b.
Dilation
Rotation
c.
d.
Translation
Reflection
____ 22. Which sequence of transformations shows that figures A and B are congruent?
a.
b.
c.
d.
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.
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.
____ 23. Refer to the figure shown. Which of the following statements is true?
a.
b.
TUV  WXV by SAS
TUV  WXV by SSS
c.
d.
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TUV  VWX by SAS
TUV  XWV by ASA
Name: ________________________
ID: B
____ 24. If two polygons are SIMILAR, then the corresponding sides must be _____.
a. proportional
c. parallel
b. similar
d. congruent
____ 25. 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)  (x,y), followed by a rotation: (x,y)  (y,x).
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)  (y,x), followed by a reflection: (x,y)  (x,y).
ABC 
____ 26.
a.
b.
29
87
b.
c.
d.
by a rotation:
by a translation:
by a rotation:
EDF . Find f.
c.
d.
58
35
____ 27. What is the best first step when finding a sequence of rigid motions to map
a.
by a reflection:
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 angle of ABC to the corresponding angle of
another triangle AB C .
Find a single transformation that maps one side of ABC to the corresponding side of
DEF .
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Name: ________________________
ID: B
____ 28. Which describes the transformation from the original to the image, and tells whether the
two figures are similar or congruent?
a.
b.
translation, congruent
translation, similar
c.
d.
reflection, congruent
dilation, similar
____ 29. Which is the image of  4,7  rotated 180 about the origin?
a.  4,7 
c.  7,4 
b.  7,4 
d.  4,7 
____ 30. ABC and DEF have the following properties: AB  DE , BC  EF ,
and B  E .
If AB = 18, BC = 13, and mB = 45, and DE = n + 12, EF = 3n – 5, and
mE = (5n + 15)°, determine the value of n.
a. n = 11
c. n = 9
b. n = 6
d. n = 13
9
Name: ________________________
ID: B
____ 31. This drawing illustrates ______.
a.
b.
SSS Similarity
SAS Similarity
c.
d.
AA Similarity
SAS Congruence
c.
d.
x  9.75 y  10.2
x  8.75 y  11.2
____ 32. Given that ABC  DEF solve for x and y.
a.
b.
____ 33. If
a.
b.
c.
d.
x  9.75 y  11.2
x  8.75 y  10.2
ABC 
GHI , what is the length of GH ?
13
10
23
The length cannot be determined.
10
Name: ________________________
ID: B
____ 34. What single rigid motion can move the solid figure onto the dashed figure?
a.
b.
dilation
translation
c.
d.
reflection
rotation
____ 35. 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  2) followed by (x, y)  (x, y)
(x, y)  (x, y  2) followed by (x, y)  (x,  y)
(x, y)  (x,  y) followed by (x, y)  (x, y  2)
(x, y)  (x, y) followed by (x, y)  (x, y  2)
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Name: ________________________
ID: B
____ 36. Write a congruence statement for the pair of congruent polygons.
a.
b.
c.
d.
Quadrilateral EFGH  quadrilateral MNKL
Quadrilateral EFGH  quadrilateral NKLM.
Quadrilateral EFGH  quadrilateral KLMN
Quadrilateral EFGH  quadrilateral LMNK
____ 37. Which coordinate notation correctly describes a transformation that maps the black triangle to the gray
triangle?
a.
b.
c.
d.
The translation  x, y    x  4, y  8 
The rotation  x, y    y,  x 
The rotation  x, y    x,  y 
The translation  x, y    x  6, y  2 
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Name: ________________________
ID: B
____ 38. Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points.
D: (x,y)  (0.5x,0.5y)
J(1, 4), K(6, 4), L(6, 1), M(1, 1)
a.
b.
J´(0.5, 2), K´(3, 2),
L´(6, 1), M´(1, 1)
J´(2, 0.5), K´(2, 3),
L´(0.5, 3), M´(0.5, 0.5)
c.
d.
J´(–0.5, –2), K´(–3, –2),
L´(–3, –0.5), M´(–0.5, –0.5)
J´(0.5, 2), K´(3, 2),
L´(3, 0.5), M´(0.5, 0.5)
____ 39. 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, similar
c.
d.
translation, congruent
dilation, similar
____ 40. One way to show that two triangles are similar is to show that ______.
a. an angle of one is congruent to an angle of the other
b. two sides of one are proportional to two sides of the other
c. a side of one is congruent to a side of the other
d. two angles of one are congruent to two angles of the other
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Name: ________________________
ID: B
____ 41. If line m  line n and 2 measures 35, what is the measure of 5?
a.
b.
55
145
c.
d.
155
180
c.
d.
4
8.5
____ 42. ABCD  LMNO. What is the value of r?
a.
b.
9
6.5
____ 43. Obtuse triangle ABC  obtuse triangle DEF. mA = 104 and mF = 32. Find mB.
a. 32
c. 44
b. 42
d. 104
____ 44. Given AB  DE , B  E , and BC  EF , which is a good first step when proving that
a.
b.
c.
d.
Translate ABC so it maps onto DEF .
Find a sequence of rigid motions that maps AB onto DE .
Find a sequence of rigid motions that maps A onto F .
Find a sequence of rigid motions that maps AB onto BC .
14
ABC 
DEF ?
Name: ________________________
____ 45. Determine whether triangles
a.
b.
c.
d.
ID: B
EFG and
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)  (x,y).
The triangles are congruent because
(x,y)  (y,x).
PQR are congruent.
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 reflection:
EFG can be mapped to
PQR by a rotation:
15
Name: ________________________
____ 46.
ID: B
JKL is translated using (x,y)   x  1,y  3  after it is reflected across the x-axis. What are the
coordinates of the final image of point J under this composition of transformations?
a.
b.
 6, 1 


 1,6 


c.
d.
 6,1 


 1, 6 


____ 47. The transformation:  x, y    x  5, y  7  is a __________.
a. Reflection
b. Dilation
c. Translation
d. Rotation
____ 48. When the point  3,2  is reflected across the y-axis, what is the resulting image?
a.  3, 2 
c.  3, 2 
b.  3,2 
d.  2, 3 
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Name: ________________________
ID: B
____ 49. Are rectangles ABCD and WXYZ congruent? If so, what is a sequence of transformations that maps ABCD to
WXYZ ?
a.
b.
c.
d.
Yes; reflect across the x-axis and then translate 8 units left.
Yes; reflect across the y-axis and then rotate 90 counterclockwise about the origin.
Yes; rotate 90 clockwise about the origin and then translate 8 units left.
No; there is no sequence of transformations that maps ABCD to WXYZ.
____ 50. 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
17