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Proving and Using Congruent Triangles

Total questions: 40

Worksheet time: 1hrs 20mins

Name
Class
Date
1.

Including the Reflexive Property, state whether the triangles are congruent and why.

a)

no, not enough information

b)

yes, SAS

c)

yes, ASA

d)

yes, HL

2.

Including Vertical Angles are Congruent, state whether the triangles are congruent and why.

a)

yes, AAS

b)

yes, SAS

c)

yes, ASA

d)

no, not enough information

3.

Including the Reflexive Property, state whether the triangles are congruent and why.

a)

yes, SSS

b)

yes, ASA

c)

yes, AAS

d)

yes, HL

4.
State if the triangles are congruent and why.
a)
Not congruent
b)
AAS
c)
SSS
d)
ASA
5.
State if the triangles are congruent and why.
a)
AAS
b)
ASA
c)
Not congruent
d)
SSS
6.

Using the fact that Vertical Angles are congruent, state whether the triangles are congruent and why.

a)

yes, ASA

b)

yes, AAS

c)

yes, SAS

d)

Not congruent, not enough information.

7.

Including the Reflexive Property, which theorem proves the triangles are congruent.

a)

ASA

b)

SSS

c)

SAS

d)

AAS

8.

Using the Reflexive Property, which theorem proves that the triangles are congruent.

a)

SAS

b)

AAS

c)

ASA

d)

HL

9.

Using the fact that Vertical Angles are congruent, state whether the triangles are congruent and if so, why.

a)

yes by HL

b)

yes, by SAS

c)

No, not congruent there is no AAA theorem

d)

yes, by AAS

10.

What additional information is needed to prove the triangles congruent by HL?

a)

A

b)

B

c)

C

d)

D

11.

What additional information is needed to prove the triangles congruent by SSS?

a)

A

b)

B

c)

C

d)

D

12.
Can the triangles be proven congruent?  If so, how?
a)
ASA
b)
AAS
c)
SAS
d)
Cannot be proven congruent
13.
What missing piece of information is needed to prove the triangles congruent using ASA?
a)
GC = CD
b)
CE = CD
c)
∠GCE≅∠BCE
d)
BD = GE
14.
What missing piece of information is needed to prove the triangles congruent using SAS?
a)
∠F≅∠Q
b)
∠G≅∠R
c)
∠H≅∠S
d)
FH = QS
15.
Name the postulate, if possible, that makes the triangles congruent.
a)
SSS
b)
ASA
c)
AAS
d)
Not Possible
16.
Name the postulate, if possible, that makes the triangles congruent.
a)
SAS
b)
ASA
c)
AAS
d)
Not Possible
17.
Name the postulate, if possible, that makes the triangles congruent.
a)
SSS
b)
SAS
c)
ASA
d)
AAS
18.
Can the triangles be proven congruent?  If so, how?
a)
ASA
b)
AAS
c)
SAS
d)
Cannot be proven congruent
19.
What missing piece of information is needed to prove the triangles congruent using SAS?
a)
NM = AM
b)
NL = CA
c)
∠M≅∠B
d)
∠N≅∠C
20.
Is Angle-Angle-Angle (AAA), a valid rule for proving triangles congruent?
a)
No
b)
Sometimes
c)
Yes
d)
N/A
21.
Can the triangles be proven congruent?  If so, how?
a)
ASA
b)
AAS
c)
SAS
d)
Cannot be proven congruent
22.
Name the postulate, if possible, that makes the triangles congruent.
a)
SSS
b)
SAS
c)
ASA
d)
Not Possible
23.
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.
24.
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.
25.
What postulate proves these triangles congruent?
a)
SAS
b)
HL
c)
AAS
d)
ASA
26.
Which is NOT a test to prove triangles congruent?
a)
SAA
b)
SSS
c)
SSA
d)
SAS
27.
Complete the congruence statement.
a)
OEG
b)
OGE
c)
EGO
d)
GOE
28.
∆ABC≅∆XYZ
which is true?
a)
AB≅XY
b)
AB≅YX
c)
AB≅XZ
d)
BC≅CB
29.
 ∠A = ≅
a)
∠M
b)
∠N
c)
∠L
30.
Remember order matters. Which of the following is true?
a)
∆FGH ≅ ∆VHW
b)
∆HFG ≅ ∆HWV
c)
∆HGF ≅ ∆VHW
d)
∆FGH ≅ ∆VWH
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.
If ΔDEF ≅ ΔRST, then we can conclude that DE = what?
a)
ST
b)
RS
c)
DF
d)
RT
33.
If ΔABC ≅ ΔXYZ, which statement is always true?
a)
AB = AZ
b)
∠B ≅ ∠Y
c)
∠X ≅ ∠C
d)
AC = XC
34.
If ΔABC ≅ ΔXYZ, which statement is always true?
a)
AB = YZ
b)
∠C ≅ ∠Z
c)
∠B ≅ ∠C
d)
AC = XY
35.

Explain how you would prove that line AB is congruent to line DE

a)

AAS and CPCTC

b)

SAS and CPCTC

c)

ASA and CPCTC

d)

HL and CPCTC

36.

Explain how you would prove that line AB is congruent to line DE.

a)

AAS and CPCTC

b)

SAS and CPCTC

c)

ASA and CPCTC

d)

HL and CPCTC

37.

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

a)

Yes, SAS

b)

Yes, SSS

c)

Yes, HL

d)

Yes, SSA

e)

Not Congruent

38.
What additional information is required in order to know that the triangles are congruent by HL Theorem?
a)
∠G ≅ ∠X
b)
∠H ≅ ∠V
c)
GI ≅ XV
d)
GH ≅ XW
39.

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

a)

Yes, SAS

b)

Yes, SSS

c)

Yes, HL

d)

Yes, ASA

e)

Not Congruent

40.
What is the correct congruence statement?  ΔDEC ≅________
a)
ΔAEB
b)
ΔEAB
c)
ΔBEA
d)
Not Congruent

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