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Similar Triangles SSS SAS AA

Total questions: 100

Worksheet time: 5hrs 31mins

Name
Class
Date
1.
a)
Not Similar
b)
Similar. ∆ABC~∆EDF
c)
Similar. ∆ACB~∆EDF
d)
Similar. ∆ABC~∆EFD
2.
a)
Not Similar
b)
Similar. ∆GHI~∆JKL
c)
Similar. ∆GIH~∆JKL
d)
Similar. ∆GHI~∆JLK
3.
a)
Not Similar
b)
Similar. ∆MNP~∆RQS
c)
Similar. ∆MNP~∆QRS
d)
Similar. ∆NPM~∆QRS
4.
a)
Not Similar
b)
Similar. ∆MNP~∆RQS
c)
Similar. ∆MNP~∆QRS
d)
Similar. ∆NPM~∆QRS
5.
a)
25
b)
16
c)
9
d)
7
6.
Are these triangles similar?
Angles in Triangle 1:  40⁰,60⁰, and 80⁰
Angles in Triangle 2:  40⁰,50⁰, and 90⁰
a)
Yes
b)
No
c)
There is not enough information to decide.
7.
To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree.  How tall is the tree?
a)
144 feet
b)
72 feet
c)
36 feet
8.
a)
Similar, 2 pairs of congruent angles.
∆JKL~∆LMN
b)
Similar. Side ratios proportional.
∆LMN~∆JKN
c)
Not Similar
d)
Similar. Perpendicular lines.
∆JKN~∆LMN
9.
a)
Similar, 2 pairs of congruent angles.
∆QRP~∆TRS
b)
Similar, 2 pairs of congruent angles.
∆QRP~∆SRT
c)
Not Similar
d)
Similar, 2 pairs of congruent angles.
∆QRP~∆STR
10.
The triangles are similar by...
a)
SAS
b)
AA
c)
ASA
d)
SSS
11.
Are these triangles similar?
Known angles in Triangle 1:  40⁰,60⁰
Known angles in Triangle 2:  60⁰,40⁰
a)
Yes
b)
No
c)
There is not enough information to decide.
12.
Determine whether the triangles are similar or not. If so, state how they are similar.
a)
Yes, by AA Similarity
b)
Yes, by SAS Similarity
c)
Yes, by SSS Similarity
d)
No, not similar
13.
Determine whether the triangles are similar.
a)
SSS
b)
AA
c)
SAS
d)
not similar
14.
What is the similarity statement for the triangle pair?
a)
ΔXYZ~ΔNEW
b)
ΔXZY~ΔNWE
c)
ΔZYX~ΔENW
d)
ΔYZX~ΔNWE
15.
If two figures are similar their angles are______.
a)
proportional
b)
congruent
c)
supplementary
d)
complementary
16.
If two figures are similar, the corresponding sides are ______________.
a)
equal
b)
congruent
c)
proportional
d)
none of these
17.
What is the height of the Tree?
a)
20
b)
15
c)
30
d)
10
18.
Find AE
a)
12.5
b)
18
c)
11.75
d)
13
19.
Find x.
a)
54/7
b)
56/3
c)
11
d)
21/2
20.
If the triangles are similar, find x
a)
90
b)
60
c)
30
d)
15
21.
Use the information in the diagram to determine the height of the tree.
a)
80 feet
b)
320 feet
c)
40 feet
d)
160 feet
22.
Find x.
a)
-2
b)
10
c)
4
d)
7
23.
a)
? = 11
b)
? = 22
c)
? = 12
d)
? = 2
24.
a)
15
b)
13
c)
11
d)
17
25.

Determine if triangles are similar. If so, name the shortcut that can correctly be applied.

a)

AA Similarity Theorem

b)

SSS Similarity Theorem

c)

SAS Similarity Theorem

d)

Not necessarily similar

26.

Determine if triangles are similar. If so, name the shortcut that can correctly be applied.

a)

AA Similarity Theorem

b)

SSS Similarity Theorem

c)

SAS Similarity Theorem

d)

Not necessarily similar

27.

If m< KJV = 59, determine if triangles are similar. If so, name the shortcut that can correctly be applied.

a)

AA Similarity Theorem

b)

SSS Similarity Theorem

c)

SAS Similarity Theorem

d)

Not necessarily similar

28.

Determine if triangles are similar. If so, name the shortcut that can correctly be applied.

a)

AA Similarity Theorem

b)

SSS Similarity Theorem

c)

SAS Similarity Theorem

d)

Not necessarily similar

29.

Determine if triangles are similar. If so, name the shortcut that can correctly be applied.

a)

AA Similarity Theorem

b)

AA Similarity Theorem

c)

SAS Similarity Theorem

d)

Not necessarily similar

30.

Determine if triangles are similar. If so, name the shortcut that can correctly be applied.

a)

AA Similarity Theorem

b)

SSS Similarity Theorem

c)

SAS Similarity Theorem

d)

Not necessarily similar

31.

Determine if triangles are similar. If so, name the shortcut that can correctly be applied.

a)

AA Similarity Theorem

b)

SSS Similarity Theorem

c)

SAS Similarity Theorem

d)

Not necessarily similar

32.

Determine if triangles are similar. If so, name the shortcut that can correctly be applied.

a)

AA Similarity Theorem

b)

SSS Similarity Theorem

c)

SAS Similarity Theorem

d)

Not necessarily similar

33.

Determine if triangles are similar. If so, name the shortcut that can correctly be applied.

a)

AA Similarity Theorem

b)

SSS Similarity Theorem

c)

SAS Similarity Theorem

d)

Not necessarily similar

34.

Determine if triangles are similar. If so, name the shortcut that can correctly be applied.

a)

AA Similarity Theorem

b)

SSS Similarity Theorem

c)

SAS Similarity Theorem

d)

Not necessarily similar

35.
a)

SAS~

b)

SSS~

c)

AA~

d)

Not similar ~

36.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not Similar

37.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

38.

Choose BOTH methods that can be used

a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

39.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

40.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

41.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

42.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

43.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

44.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

45.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

46.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

47.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

48.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

49.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

50.

Choose BOTH methods that can be used

a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

51.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

52.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

53.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

54.
a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

55.

Choose BOTH methods that can be used

a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

56.
Complete each proportion.
CB / DM  =  AC / ?
a)
BM
b)
MA
c)
BC
d)
AD
57.
Complete each proportion.
AB / BM  =  ? / CD
a)
BC
b)
AC
c)
MD
d)
MC
58.
What is the value of X and Y ?
a)
X=2.5 and Y=6.5
b)
X=6.5 and Y=2.5
c)
X=3 and Y=7
d)
X=2 and Y= 5
59.
Complete the similarity statement.
ABC ~ ___
a)
ZYX
b)
XZY
c)
YZX
d)
XYZ
60.
2 triangles are similar if _____________.
a)
their angles are congruent.
b)
their sides are congruent.
c)
their areas are equal.
d)
their perimeters are equal.
61.
How many pairs of congruent angles in 2 triangles are needed to prove the 2 triangles are similar?
a)
2 or 3
b)
1
c)
0
d)
only 3
62.
The measures of the angles in a triangle are 53⁰,78⁰, and 49⁰.  A similar triangle is created by using a dilation with a scale factor of 2.  What are the measures of the angles of this triangle?
a)
53⁰,78⁰, and 49⁰
b)
There is not enough information to answer this question.
c)
106⁰,156⁰, and 98⁰
d)
26.5⁰,39⁰, and 24.5⁰
63.
Similarity Ratio: _
a)
2/3
b)
1/2
c)
2
d)
3
64.
Which of the statements is true about the graphed triangles?
a)
They are similar, because the image can be obtained by dilating about the origin with a scale factor of 2.
b)
They are similar, because the image can be obtained by dilating about the origin with a scale factor of 1/2.
c)
They are not similar, because the image can be obtained by dilating about the origin with a scale factor of 2.
d)
They are not similar, because the image can be obtained by dilating about the origin with a scale factor of 1/2.
65.
What scale factor was used to produce the image?
a)
2
b)
3
c)
1/3
d)
1/2
66.
What scale factor was used to produce the image?
a)
2
b)
-2
c)
1/2
d)
1
67.
TRUE or FALSE.
When a shape is dilated, angles within the shape change. 
a)
True
b)
False
68.
TRUE or FALSE.
Rotation, translations, and dilations preserve congruence. 
a)
True
b)
False
69.
TRUE or FALSE.
When a shape is dilated, parallel lines remain parallel. 
a)
True
b)
False
70.
TRUE or FALSE.
When a shape is dilated, orientation is preserved. 
a)
True
b)
False
71.
All corresponding sides are congruent in similar figures.
a)
True
b)
False
72.

Victoria holds a 5-foot long fishing pole. The fishing line extends 3 feet to the water’s surface and then another 12.6 feet to a hook. How far is the fish from the hook?

a)

21 ft

b)

24.6 ft

c)

27 ft

d)

30.6 ft

73.
a)

Angle Bisector Theorem

b)

Alternate Interior Angle Theorem

c)

Triangle Sum Theorem

d)

Angle-Angle Similarity Theorem

74.

A super-heroine slides down a 25-yard-long wire from the top of a 20-yard-tall building into a window 2 yards below the top of a 12-yard-tall building. Her photo is taken by a photographer when she is at point A. At that moment, how far is she from the window?

a)

4 yds

b)

5 yds

c)

6 yds

d)

20 yds

75.

In triangles TUW and WXT, ∠U and ∠X are congruent. Andre wants to prove that these triangles are similar. Which of the following is a counterexample to show that triangles TUW and WXT are NOT similar?

a)

∠U ≅ ∠X, but ∠UTW is not congruent to ∠XWT

b)

∠U ≅ ∠X, but ∠UWT ≅ ∠XTW and ∠UTW ≅ ∠XWT.

c)

∠U ≅ ∠X, but ∠UWT ≅ ∠UTW and ∠XTW ≅ ∠XWT

d)

∠UWT ≅ ∠UTW, ∠XTW ≅ ∠XWT, but ∠U is not congruent to ∠X.

76.

Corrine makes a model of Earth and the Moon to show how a satellite could communicate between a base at point A, and the launch site at point E. On her model, the path from the center of the Moon, B, to the center of Earth, D, is an 18-inch-long straight line. A signal leaves the base at point A, travels to the satellite at point C, and refl ects the signal to the launch site at point E. The distance from the center of the Moon model, B, to the base, A, is 4 inches. The distance from the center of the Earth model, D, to the launch site, E, is 6 inches. In Corrine’s model, angles ABC and EDC are right angles. To the nearest inch, how far is the model satellite from the center of the Earth model?

a)

7 inches

b)

8 inches

c)

10 inches

d)

11 inches

77.

If triangles MNO and PQR are similar, which of the following must be true? Select all that apply.

a)

NM/QP =QR/NO = MO/PR = 1

b)

∠N ≅ ∠QRP, ∠M ≅ ∠QPR, ∠O ≅ ∠PQR

c)

∠N ≅ ∠PQR, ∠M ≅ ∠QPR, ∠O ≅ ∠QRP

d)

OM/RP = MN/PQ = ON/RQ

78.
Which is NOT true about similar triangles.
a)
The angles in the triangles are congruent to each other.
b)
The sides are proportional to each other.
c)
The angles in each triangle add up to 180o.
d)
The triangles must have at least one side that is the same length.
79.
If two polygons are similar, then the corresponding side lengths are ___________.
a)
congruent
b)
similar
c)
equal
d)
proportional
80.
Find AE
a)
12.5
b)
18
c)
11.75
d)
13
81.
What is the "reason" for step 5 of the proof?
a)
Angle Bisector Theorem
b)
Reflexive property
c)
CPCTC Theorem
d)
Proof
82.
What does CPCTC stand for?
a)
Corresponding Parts of Corresponding Triangles are Congruent
b)
Congruent Parts of Corresponding Triangles are Congruent
c)
Corresponding Parts of Congruent Triangles are Congruent
83.
Fill in the missing proofs.
a)
Transitive Property, SAS(Side-Angle-Side)
b)
Reflexive Property, SAS(Side-Angle-Side)
c)
Reflexive Property, Vertical Angles Thm.
d)
Transitive Property, SSS(Side-Side-Side)
84.
What is the "statement" for step 3 of the proof?
a)
AH=AN
b)
AD=AD
c)
HD=ND
d)
HD=DN
85.

Which of the following are ways to determine if triangles are similar? (multiple answers)

a)

SSS

b)

SSA

c)

AA

d)

HL

e)

SAS

86.
Find missing side
a)
5
b)
7
c)
9
d)
11
87.
Solve for X.
a)
2 ft
b)
3 ft
c)
4 ft
d)
6 ft
88.
Find y.
a)
144
b)
18
c)
72
d)
12
89.
The pair of figures is similar. Find the missing side.
a)
x = 20
b)
x = 12
c)
x = 5
d)
x = 4
90.
Using a proportion, find the height of the tree.
a)
x = 0.0625 ft.
b)
16 ft
c)
x = 16 ft.
91.
Solve for X.
a)
2 ft
b)
3 ft
c)
4 ft
d)
6 ft
92.

Find the similarity ratio for the smaller polygon to the bigger polygon in simplest form.

a)

3 : 5

b)

15 : 25

c)

1 : 2

d)

3 : 7

93.

Find the similarity ratio for the smaller polygon to the bigger polygon in simplest form.

a)

5 : 6

b)

15 : 18

c)

1 : 2

d)

3 : 5

94.

The polygons shown are similar. Solve for the value of x.

a)

8

b)

10

c)

0.5

d)

4

95.

The polygons shown are similar. Solve for the value of x.

a)

11

b)

21

c)

7.5

d)

6.5

96.

The polygons shown are similar. Solve for the value of x.

a)

10

b)

6

c)

16

d)

14

97.

The polygons shown are similar. Solve for the value of x.

a)

11

b)

24

c)

8

d)

9

98.
a)

x = 5

b)

x = 18

c)

x = 9/2

d)
99.

What is your teacher's real name?

a)

Mr. Wiz

b)

Mr. Wizdahl

c)

Mr. Wisdoll

d)

Mr. Wisdahl

e)

Mr. Wizdoll

100.

Which of the following is Mr. Wiz's cat, Bruno? (currently being held hostage in Florida by Mr. WIz's Dad)

a)
b)
c)
d)

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