Parallel And Perpendicular Lines Worksheet Page 45
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50Chapter 3 Study Guide and Review
Chapter 3 Study Guide and Review
3-2
3-2
Angles and Parallel Lines
See pages
Concept Summary
133–138.
•
Pairs of congruent angles formed by parallel lines and a transversal are
corresponding angles, alternate interior angles, and alternate exterior angles.
•
Pairs of consecutive interior angles are supplementary.
Example
Example
In the figure, m 1
4p
15, m 3
3p
10,
and m 4
6r
5. Find the values of p and r.
A
1
• Find p.
Since AC BD,
1 and
3 are supplementary
2
3
by the Consecutive Interior Angles Theorem.
C
B
m 1
m 3
180
Definition of supplementary angles
4
(4p
15)
(3p
10)
180
Substitution
D
7p
5
180
Simplify.
p
25
Solve for p.
• Find r.
Since AB CD,
4
3 by the Corresponding Angles Postulate.
m 4
m 3
Definition of congruent angles
6r
5
3(25)
10
Substitution, p
25
6r
5
65
Simplify.
r
10
Solve for x.
Exercises
In the figure, m 1
53. Find the
measure of each angle.
See Example 1 on page 133.
16.
2
17.
3
1
W
18.
4
19.
5
2
X
20.
6
21.
7
7
6
Y
22. In the figure, m 1
40, m 2
3a
2a
25,
5
Z
and m 3
5b
26. Find a and b.
3
4
See Example 3 on page 135.
3-3
Slopes of Lines
3-3
See pages
Concept Summary
139–144.
•
The slope of a line is the ratio of its vertical rise to its horizontal run.
•
Parallel lines have the same slope, while perpendicular lines have slopes
whose product is
1.
Example
Example
Determine whether KM and LN are parallel, perpendicular, or neither for K( 3, 3),
M( 1,
3), L(2, 5), and N(5,
4).
3
3
4
5
slope of KM: m
or
3
slope of LN: m
or
3
1
(
3)
5
2
The slopes are the same. So KM and LN are parallel.
168 Chapter 3 Parallel and Perpendicular Lines
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