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Congruent triangles

Total questions: 55

Worksheet time: 2hrs 50mins

Name
Class
Date
1.

State if the two triangles are congruent. If they are, state which theorem you would use.

a)

Yes, SAS

b)

Yes, SSS

c)

Yes, ASA

d)

No

2.

Name the postulate, if possible, that makes the triangles congruent.

a)

SAS

b)

ASA

c)

SSS

d)

Not Enough Info

3.
a)
Congruent by HL
b)
Congruent by SAS
c)
Congruent by SSS
d)
Not Necessarily Congruent
4.

Are the two triangles congruent?

a)

Not enough information

b)

Yes, by SSA

c)

Yes by SSS

d)

Yes By ASA

5.

Name the postulate, if possible, that makes the triangles congruent.

a)

SAS

b)

ASA

c)

Not Enough Info

6.

Name the postulate, if possible, that makes the triangles congruent.

a)

SSS

b)

ASA

c)

AAA

d)

Not Possible

7.

Name the postulate, if possible, that makes the triangles congruent.

a)

SSS

b)

SAS

c)

ASA

d)

Not Possible

8.

Name the postulate, if possible, that makes the triangles congruent.

a)

SAS

b)

ASA

c)

SSS

d)

Not Possible

9.
Name the postulate, if possible, that makes the triangles congruent.
a)
SSS
b)
SAS
c)
ASA
d)
Not Possible
10.
Is Angle-Angle-Angle (AAA), a valid rule for proving triangles congruent?
a)
No
b)
Sometimes
c)
Yes
d)
N/A
11.

Which of the following is not a valid reason to prove congruent triangles?

a)

SSA

b)

ASA

c)

SAS

d)

SSS

12.
Which of the following is not a valid reason to prove congruent triangles?
a)
ASA
b)
SAS
c)
SSS
d)
AAA
13.

All of the following prove triangles congruent except

a)

SSS

b)

SAS

c)

CPCTC

d)

ASA

14.
∆ABC≅∆XYZ
which is true?
a)
AB≅XY
b)
AB≅YX
c)
AB≅XZ
d)
BC≅CB
15.
∆EHG≅∆KFC
Which is a true statement?
a)
EH≅FK
b)
HG≅KF
c)
EG≅KC
d)
∠E≅∠C
16.

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

17.

Use the congruency statement to answer the following:

m∠F = ___

a)

m∠H

b)

m∠I

c)

m∠G

d)

not congruent to another angle

18.

Name the postulate, if possible, that makes the triangles congruent.

a)

SSS

b)

SAS

c)

ASA

d)

Not enough info

19.

Which of the following triangles are congruent to T

*Multiple answers*

a)
b)
c)
d)
20.

Which triangles are congruent to F

a)
b)
c)
d)

none of them

21.

Which triangles are congruent to F?

a)
b)
c)
d)

NONE of them

22.

Name the postulate, if possible, that makes the triangles congruent.

a)

SSS

b)

SAS

c)

ASA

d)

Not possible

23.

Congruent by

a)

SSS

b)

SAS

c)

ASA

d)

Not enough info

24.

Congruent by

a)

SSS

b)

SAS

c)

ASA

d)

Not enough info

25.
Which is a correct congruence statement.
a)
A
b)
B
c)
C
d)
D
26.

Are these triangles congruent? If so, state the rule which you used to determine congruence.

a)

SAS

b)

SSS

c)

Both SSS and SAS

d)

Not enough info to prove congruent

27.
Determine the Conclusion.
a)
Then ∠BCA ≅ ∠DCA.
b)
Then ∠BAC ≅ ∠DAC.
c)
Then Segment AB is congruent to Segment AD.
d)
Then ∠BAC and ∠DAC are right angles.
28.
Choose the correct conclusion.
a)
Then segment AC is congruent to segment DC.
b)
Then segment BC is congruent to segment EC.
c)
Then segment AD is congruent to Segment AD.
d)
Then Angle BCA is congruent to Angle ECD.
29.

Determine the correct conclusion from the given statement

a)

∠1 ≅ ∠4.

b)

∠2 ≅ ∠3.

c)

∠1 ≅ ∠4 AND ∠2 ≅ ∠3.

d)

Segment AB is congruent to Segment CD.

30.
If Triangle ABC is congruent to Triangle XYZ, which pair of angles are congruent?
a)
B & Z
b)
B & X
c)
A & Z
d)
C & Z
31.
Which statement indicates that the triangles in each pair are congruent.
a)
∆LMK ≅ ∆LMT
b)
∆LMK ≅ ∆TMK
c)
∆LTKM ≅ ∆LMT
d)
∆TMK ≅ ∆TLK
32.

Which of the following statements is true?

a)

∆JLK ≅ ∆XWJ

b)

∆LJK ≅ ∆JWX

c)

∆JKL ≅ ∆JXW

d)

∆LKJ ≅ ∆JXW

33.

In congruent triangles, corresponding parts are always ______.

a)

opposite

b)

congruent

c)

equilateral

d)

acute

34.

What congruency postulate proves the triangles congruency?

a)

SAS

b)

ASA

c)

SSS

d)

Not enough info

35.

What postulate proves these triangles congruent?

a)

SAS

b)

HL

c)

Not enough info

d)

ASA

36.
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)
37.
What is reason #2?
a)
Vertical angles are congruent.
b)
Consecutive angles are congruent.
c)
Alternate interior angles are congruent.
d)
Definition of Bisect
38.
What is statement #6?
a)
BC≅BC
b)
BC≅DA
c)
∠BCD≅BAC
d)
AB≅CD
39.
What is the "statement" for step 3 of the proof?
a)
HA=HA
b)
HA=AH
c)
MA=AM
d)
MA=MA
40.
What is the "reason" for step 5 of the proof?
a)
Angle Bisector Theorem
b)
Reflexive property
c)
CPCTC Theorem
d)
Proof
41.
What is the "statement" for step 3 of the proof? 
a)
∡EDA≅∡DCB
b)
∡AED≅∡BEC
c)
DE=CE
d)
∡AED≅∡CED
42.
What is the "statement" for step 2 of the proof?
a)
∆BAC≅∆DAC
b)
BC=DC
c)
∡B≅∡D
d)
∡BAC≅∡DAC
43.
What is the "reason" for step 3 of the proof?
a)
Proof
b)
Def. of Midpoint
c)
Reflexive Property
d)
Vertical angle Theorem
44.
What is the "statement" for step 3 of the proof?
a)
AD=DA
b)
AD=AD
c)
HD=ND
d)
HD=DN
45.
What would be the correct "given" statements for this diagram?
a)
T is the midpoint of segment BG and
∡B≅∡G
b)
∡B≅∡G and ∡A≅∡W
c)
T is the midpoint of segment BG and ∡A≅∡W
d)
T is the midpoint of segment AW and ∡A≅∡W
46.

What statement should go into #4?

a)

LM‾≅OP‾\overline{LM}\cong\overline{OP}

b)

N is the midpoint of MO‾N\ is\ the\ midpoint\ of\ \overline{MO}

c)

MN‾≅ON‾\overline{MN}\cong\overline{ON}

d)

LN‾≅PN‾\overline{LN}\cong\overline{PN}

47.
Identify the  missing statement or reason
a)
Given
b)
Vertical Angles Theorem
c)
Definition of Angle Bisector
d)
Alternate Interior Angles Theorem
48.
Identify the  missing statement or reason
a)
Definition of Angle Bisector
b)
Alternate Interior Angles Theorem
c)
Reflexive Property
d)
Definition of Midpoint
49.
What is the correct choice for Statement 5?
a)
SAS
b)
Definition of Congruence
c)
Prove
d)
CPCTC
50.
If L is the midpoint of TJ, what must be true?
a)
TL=JT
b)
JL=TJ
c)
TL=LJ
d)
T is also the midpoint of JL
51.
If DA bisects IE, then
a)
ID=ED
b)
IA=EA
c)
<IDA=<EDA
d)
<IAD and <EAD are right angles
52.
If AD bisects <EDI, then
a)
<ADE=<IDA
b)
IA=AE
c)
ID=ED
d)
All of the above
53.
If DA is perpendicular to IE, then we can immediately conclude that
a)
IA=AE
b)
<IAD = <DAE
c)
<IDA=<EDA
d)
<IAD and <DAE are right angles
54.

In this picture, we know for sure that

a)

<TEB=<ETS

b)

<BTE=<SET

c)

BE=ST

d)

BE=ST and <BET=<STE

55.
What additional information is required for the 2 triangles to be congruent by ASA?
a)
A
b)
B
c)
C
d)
D

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