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Geometry / Trig 2
Name __________________________
3.2 Properties of Parallel Lines & Proofs
Date ___________________________
Homework
t
1
Proof #1
Proof of Alternate Exterior Angles congruent:
Given:
l || m
Prove:
1  3
l
2
m
3
Statements
Reasons
1. ________________________________
1. ______________________________
2.
2. _____________________________
1  2
3. ________________________________
3. If lines are parallel, then corresponding
angles are congruent.
4. ________________________________
4. _____________________________
t
Proof #2
1
Proof of Same-Side Exterior Angles supplementary:
Given:
l || m
Prove:
1 is supplementary to 3
2
m
3
Statements
l
Reasons
1. ________________________________
1. ______________________________
2.
______ + ______ = 180
2.
3.
m2 = m3; 2  3
3. _____________________________
_____________________________
_____________________________
4.
______ + ______ = 180
4. _____________________________
5. ________________________________
5. Definition of ___________________
Angle Addition Postulate
Geometry / Trig 2
3.2 Properties of Parallel Lines & Proofs
Homework
t
Proof #3
2
Given:
k || l
Prove:
1 is supplementary to 7
1
4
3
6
k
5
8
l
7
Statements
Reasons
1. ________________________________
1. ______________________________
2.
2. If lines are parallel, then alternate
interior angles are congruent.
1  ____ ; ______ = ______
3. ________________________________
3.
Angle Addition Postulate
4. ________________________________
4.
5. ________________________________
5. _____________________________
Substitution
a
Proof #4
1
Given:
a || b ; c || d
Prove:
6  11
5
9
13
Statements
b
2
6
10
14
3
7
11
15
12
16
4
8
c
d
Reasons
1.
a || b
1. ______________________________
2.
6  8
2. _____________________________
_____________________________
_____________________________
3. ________________________________
3.
Given
4. ________________________________
4. If lines are parallel, then alternate
interior angles are congruent.
5. ________________________________
5. _____________________________
Geometry / Trig 2
3.2 Properties of Parallel Lines & Proofs
Homework
a
Proof #5
Given:
a || b ; c || d
Prove:
4 is supplementary to 9
1
5
9
13
Statements
10
14
b
2
6
3
7
11
15
4
8
12
16
1.
Given
2.
2.
Vertical Angle Theorem
3.
___  ___; m___ = m___
d
Reasons
1. ________________________________
4  ___; m4 = m___
c
3. _____________________________
_____________________________
_____________________________
4.
4  5; m4 = m5
4. _____________________________
5. ________________________________
5.
6.
6. If lines are parallel, then ___________
5 and 9 are supplementary
Given
______________________________
7. ________________________________
7.
Definition of supplementary angles
8. ________________________________
8. _____________________________
9. ________________________________
9. Definition of ____________________