Honors Geometry Chapter 3 – Proofs Involving Parallel and Perpendicular Lines
Practice – Proofs Involving Parallel and Perpendicular Lines No Textbook Correlation
Name ________________________ Date ________________ Period _______
Choose the word(s) that best completes the statements.
1. If two lines are cut by a transversal so that alternate interior angles are (congruent, supplementary,
complementary), then the lines are parallel.
2. If two lines are cut by a transversal so that same-side interior angles are (congruent, supplementary,
complementary), then the lines are parallel.
3. If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding) angles
are congruent, then the lines are parallel.
4. If two coplanar lines are perpendicular to the same line, then the two lines are (perpendicular, parallel,
skew) to each other.
a || b. State the postulate or theorem that justifies each conclusion.
Example:
48
because || lines corresponding s
5.
18
_________________________________
6.
37
_________________________________
7.
4
supplementary to
6
_________________________________
8.
3
supplementary to
4
_________________________________
9.
76
________________________________
State the postulate or theorem (shorthand) that allows you to conclude that j || k.
Example: corr.
‘s // lines
10. ________________ 11. ________________ 12. ________________ 13. ________________
________________ ________________ ________________ ________________
Use the figure and the given information to determine which lines, if any, are parallel. Justify using
a theorem or postulate.
14.
9 16
___ || ___ because ________________________
15.
57
___ || ___ because _________________________
16.
14 16
___ || ___ because _______________________
17.
1 16
___ || ___ because _______________________
18.
5 10
___ || ___ because ________________________
1
j
k
75
75
j
k
110
70
j
k
120
120
80
80
j
k
a
d
b
c
1
5
2
3
7
6
16
8
4
13
12
11
10
9
15
14
Honors Geometry: Chapter 3 – Proofs Involving Parallel and Perpendicular Lines
Fill in the missing statements and reasons in each proof shown below. You must mark the diagram
for credit.
19. Given:
ab
Statements Reasons
cd
1) 1) given
Prove:
1 16
2)
18 
2)
3) 3) given
4)
8 16
4)
5) 5) Transitive prop.
20. Given:
ab
Statements Reasons
cd
1) 1) given (be careful)
Prove:
98
2)
96
2)
3) 3) given
4) 4)
5)
98
5)
21. Given:
ab
cd
Prove:
2 11 180
o
mm
Statements Reasons
1) 1) given
2)
2 & 3
are supplementary 2)
3)
3)
4) 4)
5)
5)
6) 6)
7)
7)
a
d
b
c
1
5
2
3
7
6
16
8
4
13
12
11
10
9
15
14
a
d
b
c
1
5
2
3
7
6
16
8
4
13
12
11
10
9
15
14
a
d
b
c
1
5
2
3
7
6
16
8
4
13
12
11
10
9
15
14
Honors Geometry: Chapter 3 – Proofs Involving Parallel and Perpendicular Lines
22. Given:
lm
17
Prove:
ab
Statements Reasons
1)
lm
1) given
2) 2)
3) 3)
4) 4)
5) 5)
23. Given:
ab
5
is supplementary to
2
Prove:
lm
Statements Reasons
1)
5
supplementary
2
1)
2) 2)
3)
ab
3)
4)
15 
4)
5) 5)
6)
1 2 180
o
mm
6)
7) 7)
8)
lm
8)
24. Given:
12
pq
Prove:
qa
Statements Reasons
1) 1)
2) 2)
3) 3)
4) 4)
2
m
b
a
l
1
3
4
7
5
6
2
m
b
a
l
1
3
4
7
5
6
2
q
a
p
1
Honors Geometry: Chapter 3 – Proofs Involving Parallel and Perpendicular Lines
25. Given:
2&1
are Complementary
Prove:
WXSX
Statements Reasons
1)
1& 2
are Complementary 1)
2)
1 2 90mm
2)
3)
12m WXS m m
3)
4)
90m WXS
4)
5)
WXS
is right 5)
6)
SX WX
6)
26. Prove the statement: If two parallel lines are cut by a transversal, then the same-side exterior angles
are supplementary.
Given: _________________________
Prove: _________________________
Statements Reasons
1) 1)
2) 2)
3)
3)
4) 4)
5) 5)
6) 6)
7) 7)
27. Prove the statement: If two coplanar lines are perpendicular, then they form a pair of congruent,
supplementary angles.
First write the given(hypothesis) and the prove(conclusion) using the diagram.
Given: _________________________
Prove: _________________________ and ____________________________
Statements Reasons
1) 1)
2) 2)
3) 3)
4) 4)
5) 5)
6) 6)
W
X
S
•
•
1
2
2
n
a
m
1
3
2
m
n
1