Parallel And Perpendicular Lines Worksheet Page 31
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50In Lesson 3-3, you learned that parallel lines have the same slope. You can use the
slopes of lines to prove that lines are parallel.
Slope and Parallel Lines
Example
Example
4
4
g f
Determine whether
.
g
y
1
( 0, 4 )
( 6, 4 )
4
0
4
f
slope of
f
: m
or
6
3
3
4
0
4
g
slope of
: m
or
( 3, 0 )
0
(
3)
3
O
x
( 3, 0 )
g f
Since the slopes are the same,
.
Concept Check
1. Summarize five different methods to prove that two lines are parallel.
2. Find a counterexample for the following statement.
m
t
If lines and
are cut by transversal
so that consecutive interior angles are
m
t
congruent, then lines
and
are parallel and
is perpendicular to both lines.
3.
OPEN ENDED
Describe two situations in your own life in which you encounter
parallel lines. How could you verify that the lines are parallel?
Guided Practice
p
q
Given the following information, determine
1 2
which lines, if any, are parallel. State the
5 6
3 4
postulate or theorem that justifies your answer.
8 7
16
3
4
13
4.
5.
13 14
10 9
6. m 14
m 10
16 15
180
7.
1
7
11 12
m
Find x so that
m.
8.
9.
( 7 x
3 )
˚
( 9 x
5 )
˚
( 5 x
90 )
˚
( 14 x
9 )
˚
m
m
10.
Write a two-column proof of Theorem 3.5.
PROOF
p q
11. Determine whether
.
y
6
p
(
)
7
D
4
6
,
(
1
)
4
C
4
,
2
x
O
8
4
2
6
q
B
( 0,
2 )
4
A
( 7,
3 )
6
Application
12.
PHYSICS
The Hubble Telescope gathers
parallel light rays and directs them to a central
focal point. Use a protractor to measure several
of the angles shown in the diagram. Are the lines
parallel? Explain how you know.
154 Chapter 3 Parallel and Perpendicular Lines
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