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Congruency and Similarity Test

Total questions: 72

Worksheet time: 3hrs 42mins

Name
Class
Date
1.
Are these triangles similar?
a)
Yes
b)
No
2.
The pair of figures is similar. Find the missing side.
a)
x = 12
b)
x = 3
c)
x = 40
d)
x = 4
3.
The pair of figures is similar. Find the missing side.
a)
x = 20
b)
x = 12
c)
x = 5
d)
x = 4
4.
The triangles are congruent. Which of the following statements must be true?
a)
∠A ≅ ∠D
b)
∠B ≅ ∠E
c)
AB ≅ DE
d)
BC ≅ FD
5.
The two right triangles below are similar. What is x, the missing side length in triangle DEF? 
a)
3.75
b)
9.75
c)
10
d)
12
6.
Are the two figures similar?
a)
yes
b)
no
7.
Two objects that are the same shape but not the same size are _______.
a)
Congruent
b)
Vertical
c)
Similar
d)
Complementary 
8.
When talking about figures on a coordinate plane, what does "congruent" mean?
a)
Same shape, same size
b)
Same shape, size changes
c)
Different shape, different size
d)
Same shape, different size
9.
Tell whether the two figures are similar. Explain your reasoning.
a)
Yes, similar because they are the same shape and side lengths are proportional.
b)
No, not similar because they are the same shape, but side lengths are not proportional.
c)
Yes, same shape
d)
No, different sizes
10.

Are the triangles similar? If so, what is the scale factor from ΔDEF to ΔABC?

a)

Yes. 1.5

b)

Yes. ⅔

c)

Yes. 2

d)

No.

11.
Triangle ABC and XYZ are similar.  Use your knowledge of scale factor to find the length of X.
a)
20
b)
25
c)
100
d)
40
12.
Complete each proportion.
CB / DM  =  AC / ?
a)
BM
b)
MA
c)
BC
d)
AD
13.
The triangles are similar, solve for the question mark.
a)
8
b)
12.5
c)
18
d)
24
14.
Determine if the triangles are similar. Justify.
a)
Yes, by SSS.
b)
Yes, by SAS. Scale Factor is 1:2.
c)
Yes, by SAS. Scale Factor is 3:1.
d)
No, not similar.
15.

 ΔVUT≅ΔVLM\Delta VUT\cong\Delta VLM  
State the postulate that proves these triangles are similar. 

a)

SSS

b)

AA

c)

SAS

d)

Not similar

16.
Which of the following statements is true?
a)
∆BCA ≅ ∆DEF
b)
∆EFD ≅ ∆BAC
c)
∆ABC ≅ ∆FED
d)
∆EDF ≅ ∆BAC
17.
Which is NOT a test to prove triangles congruent?
a)
SAA
b)
SSS
c)
SSA
d)
SAS
18.

Are the triangles congruent, if yes, why?

a)

SSS

b)

SAS

c)

ASA

d)

Not Congruent

19.

Which triangles are congruent to D?

a)
b)
c)
d)

NONE of them

20.

Which triangle has SAS with this triangle?

a)
b)
c)
21.

Which triangle has HL similarity with this one?

a)
b)
c)
22.
Are Triangle ABC and Triangle XYZ similar?
a)
No, corresponding angles are not congruent
b)
No, corresponding sides are not proportional
c)
Yes, corresponding angles are congruent
d)
Yes, corresponding sides are proportional
23.
Triangle ABC is congruent to Triangle XYZ.  What side corresponds to XZ?
a)
BC
b)
AB
c)
AC
d)
XY
24.
What side corresponds to ED?
a)
TA
b)
NA
c)
TN
d)
RD
25.
Are the triangles congruent, if yes, why?
a)
SSS
b)
SAS
c)
ASA
d)
Not Congruent
26.
Are the triangles congruent, if yes, why?
a)
SAS
b)
ASA
c)
SSS
d)
Not Congruent
27.
Are the triangles congruent, if yes, why?
a)
SSS
b)
ASA
c)
AAA
d)
Not Congruent
28.
Name the postulate, if possible, that makes the triangles congruent.
a)
SAS
b)
ASA
c)
AAS
d)
Not enough information
29.

"If three sides of one triangle are proportional to three sides of another triangle, then the two triangles are similar," is describing which similarity postulate?

a)

AAA

b)

SAS

c)

Not similar

d)

SSS

30.

"If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar," is describing which Similarity Postulate?

a)

SSS

b)

AA

c)

ASA

d)

SAS

31.
If two figures are similar, the corresponding sides are ______________.
a)
equal
b)
congruent
c)
proportional
d)
none of these
32.
If two figures are similar their angles are______.
a)
proportional
b)
congruent
c)
supplementary
d)
complementary
33.
What pattern could you use to prove the triangles congruent?
a)
SSS
b)
SAS
c)
ASA
d)
AAS
34.

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, Then the two triangles are congruent.

a)

Angle-Side-Angle Postulate

b)

Angle-Angle-Side Theorem

35.
∆EHG≅∆KFC
Which is a true statement?
a)
EH≅FK
b)
HG≅KF
c)
EG≅KC
d)
∠E≅∠C
36.

Whats is the symbol for Congruency

a)
b)
c)
d)
37.

what is symbol for similarity

a)
b)
c)
d)
38.
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
39.
a)
Not Similar
b)
Similar. ∆MNP~∆RQS
c)
Similar. ∆MNP~∆QRS
d)
Similar. ∆NPM~∆QRS
40.

Find Y.

a)

25

b)

4

c)

9

d)

7

41.

Consider the triangles shown. Which can be used to prove the triangles are congruent?

a)

SSS

b)

ASA

c)

SAS

d)

AAS

42.

In this figure, LN is perpendicular to KM. What additional information would a student need to prove ∆KLN~∆MLN?

a)
b)
c)
d)
43.

In this diagram, STU is an isosceles triangle where ST is congruent to UT. The paragraph proof shows that angle S is congruent to U. Which step is missing in the proof?

a)

CPCTC

b)

Reflexive Property

c)

Definition of right angles

d)

Angle Congruence Postulate

44.
a)

Alternate interior angles are congurent

b)

Corresponding angles are congruent

c)

Vertical angles are congruent

d)

Alternate exterior angles are congruent

45.
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
46.
Find x
a)
10.5
b)
5
c)
8.5
d)
6
47.
Why are the triangles similar?
a)
AA~
b)
SAS~
c)
SSS~
d)
AAS~
48.
An NBA basketball court (rectangle) is similar to an elementary school basketball court. The sideline of the NBA court  is 94 feet, and the sideline of the elementary court is 84.6 feet. The NBA court has a perimeter of 288 ft. Find the perimeter of the elementary court.
a)
288 feet
b)
5802 feet
c)
259 feet
d)
275 feet
49.
Are the triangles similar? If so, what similarity shortcut is used? Show all work.
a)
Similar.  SAS
b)
Similar.  AA
c)
Similar. SSS
d)
Not Similar
50.
All corresponding sides are congruent in any similar figure.
a)
True
b)
False
51.
All corresponding angles are congruent in similar figures.
a)
True
b)
False
52.
All corresponding sides are proportional (same ratio) in similar figures.
a)
True
b)
False
53.
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
54.
A building is 20 feet tall and casts a 12 foot shadow, and a person who is standing right next to the building casts a 3 foot shadow, how tall would the person be?
a)
15 feet
b)
20 feet
c)
2.5 feet
d)
5 feet
55.

Which postulates can we use to prove triangles are congruent

(Select all that apply)

a)

ASA

b)

SSA

c)

SAS

d)

SSS

56.

Which postulates can we use to prove Triangles are similar

(Select all that apply)

a)

SAS

b)

ASA

c)

SSS

d)

AA

57.

What theorem can be used to prove two right triangles are congruent?

a)

Triangle Proportionality Theorem

b)

Triangle Sum Theorem

c)

Alternate Interior Angles Theorem

d)

Hypotenuse-Leg Theorem

58.
Find AE
a)
12.5
b)
18
c)
11.75
d)
13
59.
What postulate supports these triangles to be congruent?
a)
HL
b)
SSA
c)
SAS
d)
ASA
60.
What does CPCTC stand for?
a)
Congruent parts of congruent triangles are congruent
b)
Corresponding parts of congruent triangles are congruent
c)
Corresponding parts of corresponding triangles are corresponding
d)
Corresponding parts of congruent triangles are Canadian.
61.
What postulate proves these triangles congruent?
a)
SAS
b)
ASA
c)
AAS
d)
Not enough information
62.
Fill in the blank.
a)
Given
b)
Reflexive Property
c)
Transitive Property
d)
They're the same side!!!!!! 
63.
Complete the congruence statement.
a)
CRP
b)
PCR
c)
RPC
d)
PRC
64.
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)
65.
What is the reason?
a)
Definition of Angle
b)
Definition of Congruence
c)
Definition of bisects
d)
Definition of midpoint
66.
What is the "reason" for step 3 of the proof?
a)
Vertical Angle Theorem
b)
given
c)
reflexive property
d)
proof
67.
What is the correct choice for Statement 1?
a)
Given
b)
Prove
c)
Definition of Congruence
d)
Reflexive Property
68.
What is the correct choice for Statement 4?
a)
Segment SU ≅ Segment VT 
b)
Prove
c)
Segment ST ≅ Segment UV
d)
Definition of Congruence
69.
What is the correct choice for Reason 2?
a)
Given
b)
Prove
c)
Reflexive Property
d)
Definition of Congruence
70.
What is the correct choice for Statement 1?
a)
segment MN ≅ segment OP
b)
Given
c)
<MNP ≅ <OPN
d)
segment MP ≅ segment NO
71.
What is the correct choice for Statement 5?
a)
SAS
b)
Definition of Congruence
c)
Prove
d)
CPCTC
72.
What is the correct choice for Statement 2?
a)
Segment GH ≅ Segment KL
b)
∠G ≅ ∠K
c)
Segment GI ≅ Segment KJ
d)
Segment HI ≅ Segment LJ

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