OPTIONAL PROOF PRACTICE (3.5 Quiz), Page 1 of 2
Given: l || m
Prove: 2 & 5 are
supplementary


(Hint: Scribble out all angles
EXCEPT  2, 4, and 5)



Reasons
1. Given
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
8.
8.
9.
9.

Statements
Reasons
Given: l || m
1 . l || m
1. Given
Prove: 2 & 7 are
supplementary
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
8.
8.
9.
9.

(Hint: Scribble out all angles
EXCEPT  2, 3, and 7)

Statements
1 . l || m


Given: ST || QR ;
1  3
Prove: 2  3

  
  
Jerg Study Guide, p. 26, #18
Statements
Reasons
1 . ST || QR ;
1. Given
2.
2. Given
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.

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OPTIONAL PROOF PRACTICE (3.5 Quiz), Page 2 of 2
Statements
Given: AB || CD
Prove:
m 4 + m 2 + m 5 = 180o
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


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1 . AB || CD
2. 4 & BAC are ___________________
2.
3.
3.

4. m BAC = ___________________________


Reasons
1. Given
4.
5.
5.
6.
6.
7.
7.
8.
8.
9.
9.
Statements
Draw 4-sided figure
ABCD.
Given: AB || CD
AD || BC 
Prove: A  C




  
1 . AB || CD
1. Given
2.
2.
3.
3.
4. AD || BC
4. Given
5.
5.
6.
6.
7.
7.
8.
8.
9.
9.
10.
10.


Reasons

Statements
Draw 4-sided figure ABCD.
Given: AB || CD
AD || BC
Prove: A  C




  
Reasons
1 . AB || CD
1. Given
2.
2.
3. AD || BC
3. Given
4.
4.
5.
5.
6.
6.




SAMPLE ANSWERS: OPTIONAL PROOF PRACTICE (3.5 Quiz), Page 1 of 2
Given: l || m
Statements
Prove: 2 & 5 are
supplementary



1. Given
2. 4 and 5 are supplementary
2. Consecutive Interior. Angles Thm
3. m 4 + m 5 = 180o
3. Definition of supplementary s
4. 2  4
4. Vertical angles theorem
5. m 2 = m 4
5. Definition of congruent angles
6. m 2 + m 5 = 180o
6. Substitution POE: line 5 & 3 (NOT trans)
7. 2 and 5 are supplementary
7. Definition of supplementary s
8.
8.



 


(Hint: Scribble out all angles
EXCEPT  2, 4, and
5)





9.

9.



Statements
Reasons
Given: l || m
1 . l || m
1. Given
Prove: 2 & 7 are
supplementary
2. m 2 + m 3 = 180o
2. Linear Pair Postulate
3. 3  7
3. Corresponding s Postulate
4. m 3 = m 7
4. Def. of congruent s
5. m 2 + m 7 = 180o
5. Substitution POE: line 4 & 2 (NOT trans)
6. 2 and 7 are supplementary
6. Definition of supplementary s
7.
7.



 


(Hint: Scribble out all angles

EXCEPT  2, 3, and 7)

Reasons
1 . l || m

8.



8.

9.


9.

Statements
Reasons
Given: ST || QR ;
1  3
1 . ST || QR ;
1. Given
Prove: 2  3
2. 1  3
2. Given
3. 1  2
3. Corresponding Angles Postulate
4. 2  3
4. Transitive POC (NOT substitution)
5.
5.
6.
6.
7.
7.

  
  

  
  
  
Jerg Study Guide, p. 26, #18
SAMPLE ANSWERS: OPTIONAL PROOF PRACTICE (3.5 Quiz), Page 2 of 2
Statements
Given: AB || CD
Prove: m 4 + m 2 +
m 5 = 180o








1 . AB || CD
2. 4 and BAC are supplementary
2. Consecutive Int. ’s Thm
3. m 4 + m BAC = 180o
3. Definition of supplementary angles

4. m BAC = m 2 + m 3

5. m 4 + (m 2 + m 3) = 180o

6. 3  5



7. m 3 = m 5



8.
m
4
+
m 2 + m 5 = 180o

Jerg Study Guide, p. 28, #11
  

Reasons
1. Given
9.



4. Angle Addition Postulate

5. Substitution POE: line 4 into 3.
6. Alternate Interior Angles Thm
7. Definition of congruent angles
8. Substitution POE: line 7 into 5. NOT trans
9.

Statements
Draw 4-sided figure
ABCD.
Given: AB || CD
AD || BC 
Prove: A  C 




  





Jerg p. 82 , #23

Reasons
1 . AB || CD
1. Given
2. B and C are supplementary
2. Consecutive Interior ’s Thm
3. m B + m C = 180o
3. Def. supplementary angles
4.. AD || BC
4. Given


5. A and B are supplementary

6. m A + m B = 180o

7. m B + m C = m A + m B

8. m C = m A

9. C  A



10. A  C


5. Consecutive Interior. ’s Thm
6. Def. supplementary angles
7. Trans POE/Substit. POE (lines 3 & 6)

8. Subtraction POE
9. Def. of congruent angles
10. Symmetric POC
  
OR: An alternate Version
of This Proof is below!
  
Draw 4-sided figure
ABCD.
Given: AB || CD
AD || BC 
Prove: A  C 


 Jerg p.
82 , #23
  


Statements
Reasons
1 . AB || CD
1. Given
2. B and C are supplementary
2. Consecutive Interior ’s Thm
3. AD || BC
3. Given
4. A and B are supplementary
4. Consecutive Interior ’s Thm


5. A  C


  
NOT trans

5. Congruent Supplements Thm
