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.
1 2
3 4
a || b. State the postulate or theorem that justifies each conclusion. a
Example: 4  8 because || lines  corresponding s 
5. 1  8 _________________________________
5 6
7 8
b
6. 3  7 _________________________________
7. 4 supplementary to 6 _________________________________
8. 3 supplementary to 4 _________________________________
9. 7  6 ________________________________
State the postulate or theorem (shorthand) that allows you to conclude that j || k.
Example: corr.  ‘s   // lines
10. ________________ 11. ________________
________________
________________
12. ________________
________________
j
75
k
110
70
13. ________________
________________
j
120
j
80
k
80
k
120
75
k
j
Use the figure and the given information to determine which lines, if any, are parallel. Justify using
a theorem or postulate.
a
14. 9  16  ___ || ___ because ________________________
1
5 2
b
6
15. 5  7  ___ || ___ because _________________________
3
9
4
13
16. 14  16  ___ || ___ because _______________________
17. 1  16  ___ || ___ because _______________________
18. 5  10  ___ || ___ because ________________________
14
7
10
8
11
15 12
16
c
d
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:
a
b
Statements
Reasons
c
d
1)
1) given
2) 1  8
2)
3)
3) given
4) 8  16
4)
5)
5) Transitive prop. 
1  16
Prove:
a
1
5 2
6
13
9
10
14
b
7
15
3
4
8
11
12
16
c
d
20. Given: a
b
Statements
Reasons
c
d
1)
1) given (be careful)
2) 9  6
2)
3)
3) given
4)
4)
5) 9  8
5)
Prove: 9  8
a
1
5 2
6
b
3
4
7
8
9
13 10
14
15
11
12
16
c
d
21. Given: a
b
c
d
a
Prove: m2  m11  180o
Statements
1)
Reasons
1) given
2) 2 & 3 are supplementary 2)
3)
3)
4)
4)
5)
5)
6)
6)
7)
7)
5
1
2
6
b
3
4
7
8
9
13 10
14
15
11
12
16
c
d
Honors Geometry: Chapter 3 – Proofs Involving Parallel and Perpendicular Lines
22. Given: l m
1  7
Prove: a b
Statements
1) l m
2 3
4
1
Reasons
1) given
2)
2)
3)
3)
4)
4)
5)
5)
23. Given: a
m
l
6
5 is supplementary to 2
Prove: l m
7
5
b
m
l
b
a
2 3
4
1
a
7
5
b
6
Statements
1) 5 supplementary 2
Reasons
1)
2)
2)
3) a
b
3)
4) 1  5
4)
5)
5)
6) m1  m2  180o
6)
7)
7)
8) l
m
8)
24. Given: 1  2
p q
p
Prove: q  a
1 2
Statements
1)
Reasons
1)
2)
2)
3)
3)
4)
4)
q
a
Honors Geometry: Chapter 3 – Proofs Involving Parallel and Perpendicular Lines
25. Given: 1 & 2 are Complementary
Prove: SX  WX
S
X
2
Statements
1) 1 & 2 are Complementary
Reasons
1)
2) m1 m2  90
2)
3) mWXS  m1 m2
3)
4) mWXS  90
4)
5) WXS is right
5)
6) SX  WX
6)
•
1
W•
26. Prove the statement: If two parallel lines are cut by a transversal, then the same-side exterior angles
m
n
are supplementary.
Given: _________________________
Prove: _________________________
Statements
Reasons
1)
1)
2)
2)
3)
3)
4)
4)
5)
5)
6)
6)
7)
7)
2
1
3
a
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)
m
1 2
n