Geometry/Trig Name: _________________________
USING Parallel Line Proofs – Page 1 Date: __________________________
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h
g
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s
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2. Given: k // m
Prove: 1 is supplementary to 7
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51
84
73
k
m
t
1. Given: g // h and s // t
Prove: 2 @ 15
Statements Reasons
Statements Reasons
USING Parallel Line Proofs – Page 2
4. Given: AD // BC; 1 @ 2
Prove: AB bisects CAD
A
3
C
B
D
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2
C
D
E
B
A
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2
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3. Given: CD // BE; 3 @ 1
Prove: BE bisects DBA
Statements Reasons
Statements Reasons
PROVING Parallel Line Proofs – Page 3
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h
g
t
s
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5. Given: 4 @ 13; t // s
Prove: h // g
6. Given: AB bisects CAD; 1 @ 2
Prove: AD // BC
A
3
C
B
D
1
2
Statements Reasons
Statements Reasons
PROVING Parallel Line Proofs – Page 4
2 6
51
84
73
k
m
t
7. Given: 1 @ 8
Prove: 5 @ 7
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3 4
5 6
7 8
13 14
15 16
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11 12
b
a
c d
8. Given: c // d; 1 and 14 are supplementary
Prove: a // b
Statements
Reasons
Statements
Reasons
A
DB
2
1 3
4
5 7
6
C
E
9. Given: AB // CD; 2 @ 6
Prove: BC // DE
Parallel Line Proofs – Page 5
A
DB
2
1 3
4
5 7
6
C
E
10. Given: BC // DE; 2 @ 6
Prove: AB // CD
Statements Reasons
Statements Reasons
Parallel Line Proofs – Page 6
12. Given: 1 @ 2; 4 @ 5
Prove: 3 @ 6
HINT: First prove PQ // RS, then you should
just need one more step to get to this prove.
C
D
E
B
A
3
2
1
11. Given: BE bisects DBA; 3 @ 1
Prove: CD // BE
Q
P
T
R
S
6
4
5
2
1
3
Statements Reasons
Statements
Reasons
Geometry/Trig Name: _________________________
Practice: What two lines are parallel (if any) according to the given information?
m
n
j
k
l
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4 5
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GIVEN Parallel Lines Reason
Ex. m7 = m8 j // k A
1. m7 = m4 ___________ ___________
2. m5 + m6 = 180° ___________ ___________
3. m8 = m1 ___________ ___________
4. m10 + m7 = 180 ___________ ___________
5. m1 = m7 ___________ ___________
6. m8 + (m2 + m3) = 180 ___________ ___________
7. m1 = m4 ___________ ___________
8. m1 + m2 + m3 = 180 ___________ ___________
9. m17 = m20 ___________ ___________
10. m3 = m14 ___________ ___________
11. m2 = m13 ___________ ___________
12. m11 = m16 ___________ ___________
REASONS:
A. If corresponding angles are
congruent, then lines are parallel.
B. If alternate interior angles are
congruent, then lines are parallel.
C. If alternate exterior angles are
congruent, then lines are parallel.
D. If same side interior angles are
supplementary, then lines are parallel.
E. If same side exterior angles are
supplementary, then lines are parallel.
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