G.SRT.2 ASSESSMENT – PATTERSON
1
MULTIPLE CHOICE
1. Which of the following is not a similarity transformation?
A) Translation
B) Dilation
C) Rotation
D) Stretch
2. Which of the following is not a similarity transformation?
A) Rotation
B) Reflection
C) Shear
D) Dilation
3. Which of the following is a similarity transformation but is not an isometric transformation?
A) Dilation
B) Rotation
C) Stretch
D) Translation
4. ABC  DEF, then the scale factor from ABC to DEF is:
A)
AB
DE
B)
DE
AB
C) DE : AB
D) cannot be determined
5. RTS  DFG, then the scale factor from DFG to RTS is:
A)
DF
RT
B)
RT
DF
C) RT : DF
D) cannot be determined
Answers:
1. D
2. C
3. A
4. B
5. B
TRUE/FALSE
Determine whether the following are (T)rue or (F)alse.
1. All isometric transformations are similarity transformations.
T or F
2. Similarity transformations all preserve the shape of the figure.
T or F
3. The definition of similarity is if one figure can map onto another using only
isometric transformations.
T or F
4. Congruence is a special case of similarity, when the shape and size is the same.
T or F
5. If ABC  DEF, then AB  DE
T or F
6. If ABC  DEF, then B  E
T or F
7. If ABC  DEF, AND AB : DE is 1 : 3, then DE = 3.
T or F
G.SRT.2 ASSESSMENT – PATTERSON
2
8. If ABC  DEF, AND AB : DE is 5 : 2, then AB = 5.
T or F
9. If ABC  DEF, then FDE  CAB
T or F
10. If ABC  DEF, then mABC  mFED
T or F
11. If ABC  DEF  MNP, then B  N
T or F
12. If ABC  DEF, then
EF
AB

BC DE
T or F
13. If ABC  DEF, then
BC
AB

EF DE
T or F
14. Similarity transformations all preserve the size of the figure.
T or F
15. RO,90 T3,1 (ABC )  A ' B ' C ' , then ABC  A’B’C.
T or F
16. DO,3 T3,1 (ABC )  A ' B ' C ' , then ABC  A’B’C.
T or F
17. DO,3 Rx axis (ABC )  A ' B ' C ' , then ABC  A’B’C.
T or F
18. DO,3 Rx axis RO,180 (ABC )  A ' B ' C ' , then ABC  A’B’C.
T or F
19. D
O,
1
2
(ABC )  A ' B ' C ' , then ABC  A’B’C.
T or F
20. DO,2 (ABC )  A ' B ' C ' , then AB = 2A’B’.
T or F
21. A reflection is a similarity transformation.
T or F
22. All isometric transformations are similarity transformations.
T or F
23. All transformations are similarity transformations.
T or F
24. Dilation is an isometric transformation.
T or F
25. Stretch is a similarity transformation.
T or F
Answers:
1. T
9. T
17. T
25. F
2. T
10. T
18. T
3. F
11. T
19. T
4. T
12. F
20. F
5. F
13. T
21. T
6. T
14. F
22. T
7. F
15. T
23. F
8. F
16. T
24. F
G.SRT.2 ASSESSMENT – PATTERSON
3
SHORT ANSWER (Solve)
1. Quadrilateral AGHY  Quadrilateral BFRS. Name the corresponding congruent angles and the corresponding
ratios of the sides.
A  B, G  F, H  R, Y  S
AG GH HY YA



BF
FR RS SB
2. Two quadrilaterals are similar. The following information is known about the two quadrilaterals; N  T,
1
QR 1
 . Fill in the missing points in their corresponding places.
TS = 2NQ, MN  JT and
2
SP 2
Quadrilateral ____ N ____ ____  Quadrilateral ____ T ____ ____
Answer: Quadrilateral MNQR  Quadrilateral JTSP or Quadrilateral QNMR  Quadrilateral STJP
3. Two quadrilaterals are similar. The following information is known about the two quadrilaterals; XS = 3PQ
SU UV

and
. Fill in the missing points in their corresponding places.
QT TR
Quadrilateral ____ U ____ ____  Quadrilateral ____ T ____ ____
Answer: Quadrilateral SUVX  Quadrilateral QTRP or Quadrilateral VUSX  Quadrilateral RTQP
4. Given that NHG  JKL. Complete the following.
a) G   ______
Answer: a) L
b)
KL
JK

HG
b) NH
c) J   ______ d)
______
c) N
NG

KL
HG
______
d) JL
5. Pentagon ABCDE is similar to Pentagon JYTQP. Complete the following.
a) E   ______
b)
AB CD

JY
______
c)
TQ
PJ

CD
______
D
J
C
E
B
Y
P
Q
A
d) T   ______
Answers:
a) P
e)
CD TQ
______

DE
b) TQ
c) EA
f)
AB
JY

CD
d) C
______
e) QP
f) TQ
T
G.SRT.2 ASSESSMENT – PATTERSON
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6. Use the diagram to determine your answer.
a) Is BCD  MEH? Yes or No
b) Is BCD  MEH? Yes or No
c) Is BCD  MEH? Yes or No
Why?
Why?
Why?
B
E
M
E
C
B
B
C
M
C
E
A
D
D
H
H
O
O
D
H
M
Answers: a) Yes, DA,2 (BCD)  MEH
b) Yes, RO,90 DO,2 (BCD)  MEH
c) NOT, angles not congruent
7. Use the diagram to determine your answer.
a) Is BCD  MGH? Yes or No
b) Is BCD  MGH? Yes or No
c) Is BCD  MGH? Yes or No
Why?
Why?
Why?
B
C
C
C
G
B
G
B
M
D
M
O
H
M
G
H
D
H
Answers:
a) Yes, T3,7 (BCD)    MGH b) Yes, D
O,
c) Yes, Ry axis D
O,
1
2
(BCD)  MGH
1
2
(BCD)    MGH
O
D
G.SRT.2 ASSESSMENT – PATTERSON
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8. ABC is similar to another triangle. Provided is some information about the two triangles,
BC AB
. From

JK LJ
this information determine the triangle similarity statement.
ABC  _________
Answer: LJK
9. The two figures in each question are similar. Create the similarity statement from the diagram.
a) Pentagon ABCDE  ____________
D
J
B
P
ABC  __________
R
E
C
b)
A
B
T
G
T
Q
ABC  __________
B
Y
T
c)
A
S
R
C
A
C
Answers: a) Pentagon JYTQP
b) GRT
c) STR
10. Determine the sequence of similarity transformations that map one figure onto the other thus establishing that the
two figures are similar.
a) Determine two similarity transformations that would
map OBC onto OLK.
b) Determine two similarity transformations that would
map Quad. OKBC onto Quad. OHTR.
____________________ followed by _________________
____________________ followed by _________________
K
B
L
H
K
O
O
C
T
B
R
C
Answer: a) Dilation of ½ centered at O followed by a Rotation of 90 about O (or reversed works as well)
b) Dilation of ½ centered at O followed by a Reflection over the y axis(or reversed works as well)
G.SRT.2 ASSESSMENT – PATTERSON
6
11. Determine the sequence of similarity transformations that map one figure onto the other thus establishing that the
two figures are similar.
a) Determine two similarity transformations that would
map Quad. OKBC onto Quad. OYPL.
b) Determine two similarity transformations that would
map Quad. OKBC onto Quad. PYHQ.
____________________ followed by _________________
____________________ followed by _________________
P
L
B
K
Y
K
B
O
O
H
C
C
Y
Q
P
Answer: a) Dilation of 2 centered at O followed by Rotation of 90 about O (or reversed works as well)
b) Translation of <0,-8> followed by a Reflection over the y axis (or reversed works as well)
12. Solve for the missing information, given that the two triangles in each question are SIMILAR. (2 decimals)
a)
b)
1.5 cm
y
o 1 cm
2 cm
c)
4.5 cm
x
•
y 12 cm
o
o
10 cm
7 cm
o
x
10 cm
o
12 cm
y 12 cm
o
14 cm
•
14 cm
x
x = ___________ y = __________
d)
x = ___________ y = __________
e)
y
12 cm
o
6 cm
16 cm
x
x = ___________ y = __________
f)
•
12 cm
o
y
x
7 cm •
o 4 cm
o
8 cm
15 cm
20 cm
3 cm
o
x = ___________ y = __________
Answers
o
x
4 cm
y
x = ___________ y = __________
6 cm
x = ___________ y = __________
a) x = 3, y = 6
b) x = 2.8, y = 8.57
c) x = 14.4, y = 11.67
d) x = 1.5, y = 15
e) x = 10.5, y = 10
f) x = 8, y = 6
G.SRT.2 ASSESSMENT – PATTERSON
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13. Solve for the missing information, given that the two triangles in each question are SIMILAR. (2 decimals)
a)
b)
6.5 cm
•
c)
o
7 cm
o
9 cm
y
y
5 cm
13.5 cm
x
o
x
o
6 cm
•
6 cm
x
12 cm
2 cm
12 cm
9.75 cm
x = ___________ y = __________
x = ___________ y = __________
d)
e)
3 cm
12 cm
x
y
12.4 cm
o
y
•
5 cm
2 cm
o
•
5 cm
x
o
8 cm
7 cm
6 cm
0
x = ___________ y = __________
Answers
f)
3.2 cm
x
x = __________ y = __________
o
0
y 10 cm
o
o
x = ___________ y = __________
• y
12.25 cm
•
14 cm
x = __________ y = __________
a) x = 9, y = 10.5
b) x = 7.5, y = 8
c) x = 9, y = 7.5
d) x = 3.1, y = 9.6
e) x = 2.4, y = 2.8
f) x = 8.75, y = 7
14. What is the difference between isometric transformations and similarity transformations?
Answer: Isometric transformations preserve distances and angles, whereas similarity transformations
preserve angles and not necessarily distances.
15. Solve for x
a)
x 15

8 20
b)
x = ____________
Answers
a) x = 6
b) x = 5.5
5 x2

6
9
x = ______________
G.SRT.2 ASSESSMENT – PATTERSON
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16. Solve – The ratio of two supplementary angles is 3:5. Find the measure of each angle. (2 points)
_______ & _______
Answer
67.5 & 112.5
17. Solve – The area of a rectangle is 504 cm2. If the length and the width are in a ratio of 7:2.
(2 points)
_______ & _______
Answer
42 & 12
18. Solve – Two numbers are in ratio of 11:5. If there difference is 24, what are the two numbers? (2 points)
_______ & _______
Answer
44 & 20
19. Solve - A 24 inch piece of string is used to form a 6, 8, 10 right triangle and then used to form a square.
What is the ratio of the area of the square to the area of the triangle? (2 points)
_______ : _______
Answer
3:2
20. Solve - Three numbers are in the ratio of 4:3:7. If the smallest number is 24, what is the sum of the other
two numbers? (2 points)
________________
Answer
88
21. Solve – A 96 inch stick breaks into two pieces in the ratio of 3:5. How big is each piece? (2 points)
_______ & _______
G.SRT.2 ASSESSMENT – PATTERSON
Answer
9
36 & 60
22. Determine the proper full name for the following triangle, (Characterize by side & angle)
a) which has angle ratios 1:1:2
Answer
Right Isosceles
Name: ________________________