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E
E
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Congruent Triangles Proofs
Quiz
SSS
SAS
CPTPC
AAS
ASA
Concept Quiz
Created by: Simple Class Solutions
HL
Name ___________________________
Congruent Triangles Proofs Quiz
Date ___________ Period/Class ______
State if the two triangles are congruent. If they are congruent, state the postulate or theorem used.
1.
2.
Congruent? ________
Congruent? ________
By? _________________________
By? _________________________
3.
4.
Congruent? ________
Congruent? ________
By? _________________________
By? _________________________
State the third congruence that is needed in order to prove the triangles congruent by the given
postulate or theorem.
5.
6.
To prove congruent by ASA…
To prove congruent by AAS…
!" ≅ $"
∠!"& ≅ ∠$"'
() ≅ ()
∠*)( ≅ ∠+()
_________ ≅ _________
_________ ≅ _________
© Copyright 2018 Simple Class Solutions
Congruent Triangles Proofs Quiz (cont.)
7. Complete the two-column proof.
Given: !% ≅ $%, Z is the midpoint of !$
Prove: ∆!%$ ≅ ∆$%"
Statements
Reasons
1.
1. Given
2.
2. Given
3. !" ≅ "$
3.
4. %" ≅ %"
4.
5. ∆!%$ ≅ ∆$%"
5.
A
8. Complete the two-column proof.
C
E
Given: 45 ∥ 78, 45 ≅ 78
Prove: ∆495 ≅ ∆897
B
Statements
D
Reasons
1.
1. Given
2.
2. Given
3.
3.
4.
4.
5.
5.
P
9. Complete the two-column proof.
Given: :; ≅ <;, =; bisects ∠:;<
R
Q
Prove: := ≅ <=
S
Statements
Reasons
1.
1. Given
2.
2. Given
3.
3.
4.
4.
5.
5.
6.
6.
© Copyright 2018 Simple Class Solutions
KEY
Name ___________________________
Congruent Triangles Proofs Quiz
Date ___________ Period/Class ______
State if the two triangles are congruent. If they are congruent, state the postulate or theorem used.
1.
2.
Yes
Congruent? ________
Yes
Congruent? ________
HL
By? ________
AAS
By? ________
3.
4.
No
Congruent? ________
Yes
Congruent? ________
--By? ________
ASA
By? ________
State the third congruence that is needed in order to prove the triangles congruent by the given
postulate or theorem.
5.
6.
To prove congruent by ASA…
To prove congruent by AAS…
!" ≅ $"
∠!"& ≅ ∠$"'
() ≅ ()
∠*)( ≅ ∠+()
∠,-. ≅ _________
∠/0.
_________
∠123 ≅ _________
∠341
_________
© Copyright 2018 Simple Class Solutions
KEY
Congruent Triangles Proofs Quiz (cont.)
7. Complete the two-column proof.
Given: !% ≅ $%, Z is the midpoint of !$
Prove: ∆!%" ≅ ∆$%"
Statements
Reasons
1. !% ≅ $%
1. Given
2. Z is the midpoint of !$
2. Given
3. !" ≅ "$
3. Definition of Midpoint
4. %" ≅ %"
4. Reflection Property of Congruence
5. ∆!%" ≅ ∆$%"
5. SSS Congruence Postulate
A
8. Complete the two-column proof.
C
E
Given: 45 ∥ 78, 45 ≅ 78
Prove: ∆495 ≅ ∆897
B
Statements
D
Reasons
1. 45 ∥ 78
1. Given
2. 45 ≅ 78
2. Given
3. ∠549 ≅ ∠788
3. Alternate Interior Angles Theorem
4. ∠495 ≅ ∠798
4. Vertical Angles Theorem
5. ∆495 ≅ ∆897
5. AAS Congruence Theorem*
(or ∠459 ≅ ∠879 )
(*Can also use ASA)
P
9. Complete the two-column proof.
R
Q
Given: :; ≅ <;, =; bisects ∠:;<
Prove: := ≅ <=
S
Statements
Reasons
1. :; ≅ <;
1. Given
2. =; bisects ∠:;<
2. Given
3. ∠:;= ≅ ∠<;=
3. Definition of Angle Bisector
4. ;= ≅ ;=
4. Reflexive Property of Congruence
5. ∆:;= ≅ ∆<;=
5. SAS Congruence Postulate
6. := ≅ <=
6. CPCTC
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