7-3 Parallel and Perpendicular Lines
Learn to identify parallel, perpendicular,
and skew lines, and angles formed by a
transversal.
Course 2
7-3 Parallel
Insert Lesson
Title Here Lines
and Perpendicular
Vocabulary
perpendicular lines
parallel lines
skew lines
vertical angles
transversal
Course 2
7-3 Parallel and Perpendicular Lines
When lines, segments, or rays intersect,
they form angles. If the angles formed by
two intersecting lines are equal to 90°, the
lines are perpendicular lines.
Some lines in the same plane do not
intersect at all. These lines are parallel
lines. Segments and rays that are part of
parallel lines are also parallel.
Skew lines do not intersect, and yet they
are also not parallel. They lie in different
planes.
Course 2
7-3 Parallel and Perpendicular Lines
Reading Math
The symbol means “is parallel to.” The
symbol means “is perpendicular to.”
Course 2
7-3 Parallel and Perpendicular Lines
Additional Example 1A: Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
X
Y
V
U
W
A. UV and YV
UV  YV
Course 2
Z
The lines appear to intersect
to form right angles.
7-3 Parallel and Perpendicular Lines
Additional Example 1B: Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
X
Y
V
U
W
Z
B. XU and WZ
XU and WZ
are skew.
Course 2
The lines are in different
planes and do not intersect.
7-3 Parallel and Perpendicular Lines
Additional Example 1C: Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
X
Y
V
U
W
Z
C. XY and WZ
XY || WZ
Course 2
The lines are in the same
plane and do not intersect.
7-3 Parallel and Perpendicular Lines
Try This: Example 1A
Tell whether the lines appear parallel,
perpendicular, or skew.
X
Y
V
U
W
A. WX and XU
WX  XU
Course 2
Z
The lines appear to intersect
to form right angles.
7-3 Parallel and Perpendicular Lines
Try This: Example 1B
Tell whether the lines appear parallel,
perpendicular, or skew.
X
Y
V
U
W
Z
B. WX and UV
WX and UV
are skew
Course 2
The lines are in different
planes and do not intersect.
7-3 Parallel and Perpendicular Lines
Try This: Example 1C
Tell whether the lines appear parallel,
perpendicular, or skew.
X
Y
V
U
W
C. WX and ZY
WX || ZY
Course 2
Z
The lines are in the same
plane and do not intersect.
7-3 Parallel and Perpendicular Lines
Vertical angles are the
opposite angles formed by two
intersecting lines. When two
lines intersect, two pairs of
vertical angles are formed.
Vertical angles have the same
measure, so they are
congruent.
Course 2
7-3 Parallel and Perpendicular Lines
A transversal is a line that
intersects two or more lines.
Eight angles are formed when a
transversal intersects two lines.
When those two lines are parallel,
all of the acute angles formed
are congruent, and all of the
obtuse angles formed are
congruent. These obtuse and
acute angles are supplementary.
Course 2
1
2
3
5
4
7
6
8
7-3 Parallel and Perpendicular Lines
Reading Math
Angles with the same number of tick marks are
congruent. The tick marks are placed in the
arcs drawn inside the angles.
Course 2
7-3 Parallel and Perpendicular Lines
Additional Example 2A: Using Angle Relationships to
Find Angle Measures
Line n
A.
Course 2
line p. Find the measure of the angle.
2
2 and the 130° angle are vertical
angles. Since vertical angles are
congruent, m 2 = 130°.
7-3 Parallel and Perpendicular Lines
Additional Example 2B: Using Angle Relationships to
Find Angle Measures
Line n
B.
Course 2
line p. Find the measure of the angle.
3
3 and the 50° angle are acute angles.
Since all of the acute angles in the figure
are congruent, m 3 = 50°.
7-3 Parallel and Perpendicular Lines
Additional Example 2C: Using Angle Relationships to
Find Angle Measures
Line n
C.
Course 2
line p. Find the measure of the angle.
4
4 is an obtuse angle. Since all of the
obtuse angles in the figure are congruent,
m 4 = 130°.
7-3 Parallel and Perpendicular Lines
Try This: Example 2A
Line n
line p. Find the measure of the angle.
45° 4
5 6
2 3 135° 7
A.
Course 2
n
p
3
3 and the 45° angle are vertical
angles. Since vertical angles are
congruent, m 3 = 45°.
7-3 Parallel and Perpendicular Lines
Try This: Example 2B
Line n
line p. Find the measure of the angle.
45° 4
5 6
2 3 135° 7
B.
Course 2
n
p
6
6 and the 135° angle are obtuse
angles. Since vertical angles are
congruent, m 6 = 135°.
7-3 Parallel and Perpendicular Lines
Try This: Example 2C
Line n
line p. Find the measure of the angle.
45° 4
5 6
2 3 135° 7
C.
n
p
4
4 is an obtuse angle. In the figure, the acute and obtuse
m 4 + 45° = 180°
angles are supplementary.
–45° –45°
Subtract 45° to isolate m 4.
m
Course 2
4 = 135°
7-3 Parallel
Insert Lesson
and Perpendicular
Title Here Lines
Lesson Quiz
Tell whether the lines appear
parallel, perpendicular, or skew.
1. AB and CD
parallel
2. EF and FH
perpendicular
3. AB and CG
skew
4. How are railroad tracks and two parallel lines
alike, and how are they different?
Both are always the same distance apart, but
railroad tracks are not always straight.
Course 2
D
Homework
7-3 Worksheet