Parallel And Perpendicular Lines Worksheet Page 47
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50• Extra Practice, see pages 758–760.
• Mixed Problem Solving, see page 784.
r
s
Example
Example
If
1
8, which lines if any are parallel?
1
2
r
1 and
8 are alternate exterior angles for lines
3
5 6
4
and
s
. These lines are cut by the transversal
p
. Since
7
8
p
r
s
the angles are congruent, lines
and
are parallel by
Theorem 3.5.
Exercises
Given the following information,
determine which lines, if any, are parallel. State the
A
B
C
F
postulate or theorem that justifies your answer.
D
E
See Example 1 on page 152.
G
K
35.
GHL
EJK
H
J
36. m ADJ
m DJE
180
L
37. CF
AL, GK
AL
38.
DJE
HDJ
39. m EJK
m JEF
180
40.
GHL
CDH
3-6
3-6
Perpendiculars and Distance
See pages
Concept Summary
159–164.
•
The distance between a point and a line is measured by the perpendicular
segment from the point to the line.
Example
Example
q
r
Find the distance between the parallel lines
and
whose equations are
y
x
2 and y
x
2, respectively.
q
k
• The slope of q is 1. Choose a point on line
such as P(2, 0). Let line
be
q
k
k
perpendicular to
through P. The slope of line
is
1. Write an equation for line
.
y
mx
b
Slope-intercept form
0
( 1)(2)
b
y
0, m
1, x
2
b
k
is y
x
2
An equation for
2.
Solve for b.
k
r
• Use a system of equations to determine the point of intersection of
and
.
y
x
2
Substitute 2 for y in the original equation.
y
x
2
2
x
2
2y
4
x
0
Add the equations.
Solve for x.
y
2
The point of intersection is (0, 2).
Divide each side by 2.
• Now use the Distance Formula to determine the distance between (2, 0) and (0, 2).
2
2
2
2
d
(x
x
)
(y
y
)
(2
0)
(0
2)
8
2
1
2
1
The distance between the lines is
8 or about 2.83 units.
Exercises
Find the distance between each pair of parallel lines.
See Example 3 on page 161.
1
1
41. y
4, y
42. y
x, y
x
2x
2x
1
5
2
2
170 Chapter 3 Parallel and Perpendicular Lines
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