8-3 Line and Angle Relationships
Warm Up
Find the complement of each angle
measure.
1. 30°
60°
2. 42° 48°
Find the supplement of each angle
measure.
4. 82° 98°
3. 150° 30°
8-3 Line and Angle Relationships
Learn to identify parallel, perpendicular,
and skew lines, and angles formed by a
transversal.
8-3 Line and Angle Relationships
When lines, segments, or rays intersect,
they form angles. If the angles formed by
two intersecting lines measure 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.
8-3 Line and Angle Relationships
Reading Math
The symbol means “is parallel to.” The
symbol means “is perpendicular to.”
8-3 Line and Angle Relationships
Additional Example 1A: Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
UV and YV
UV  YV
The lines appear to intersect
to form right angles.
8-3 Line and Angle Relationships
Additional Example 1B: Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
XU and WZ
XU and WZ
are skew.
The lines are in different
planes and do not intersect.
8-3 Line and Angle Relationships
Additional Example 1C: Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
XY and WZ
XY || WZ
The lines are in the same
plane and do not intersect.
8-3 Line and Angle Relationships
Check It Out: Example 1A
Tell whether the lines appear parallel,
perpendicular, or skew.
WX and XU
WX  XU
The lines appear to intersect
to form right angles.
8-3 Line and Angle Relationships
Check It Out: Example 1B
Tell whether the lines appear parallel,
perpendicular, or skew.
WX and UV
WX and UV
are skew.
The lines are in different
planes and do not intersect.
8-3 Line and Angle Relationships
Check It Out: Example 1C
Tell whether the lines appear parallel,
perpendicular, or skew.
WX and ZY
WX || ZY
The lines are in the same
plane and do not intersect.
8-3 Line and Angle Relationships
Adjacent angles have a common
vertex and a common side, but no
common interior points. Angles 2
and 3 in the diagram are adjacent.
Adjacent angles formed by two
intersecting lines are supplementary
Vertical angles are the
opposite angles formed by two
intersecting lines. Angles 1 and
3 in the diagram are vertical
angles. Vertical angles have the
same measure, so they are
congruent.
8-3 Line and Angle Relationships
Reading Math
Angles with the same number of tick marks are
congruent. The tick marks are placed in the
arcs drawn inside the angles.
8-3 Line and Angle Relationships
A transversal is a line that intersects two or more
lines. Transversals to parallel lines form special
angle pairs.
8-3 Line and Angle Relationships
Additional Example 2A: Using Angle Relationships to
Find Angle Measures
Line n
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°.
8-3 Line and Angle Relationships
Additional Example 2B: Using Angle Relationships to
Find Angle Measures
Line n
line p. Find the measure of the angle.
3
m3 + 130° = 180°
–130° –130°
m3 = 50°
Adjacent angles formed by two
intersecting lines are supplementary.
Subtract 130° to isolate m3.
8-3 Line and Angle Relationships
Additional Example 2C: Using Angle Relationships to
Find Angle Measures
Line n
line p. Find the measure of the angle.
4
Alternate interior angles are congruent.
m4 = 130°.
8-3 Line and Angle Relationships
Check It Out: Example 2A
Line n
line p. Find the measure of the angle.
45°
3
4
5 6
2 3 135° 7
n
p
3 and the 45° angle are vertical angles. Since
vertical angles are congruent, m3 = 45°.
8-3 Line and Angle Relationships
Check It Out: Example 2B
Line n
line p. Find the measure of the angle.
45°
6
4
5 6
2 3 135° 7
n
p
6 and the 135° angle are vertical angles.
m6 = 135°.
8-3 Line and Angle Relationships
Check It Out: Example 2C
Line n
line p. Find the measure of the angle.
45°
4
5 6
2 3 135° 7
4
n
m4 + 45° = 180°
–45°
–45°
m4 = 135°
p
Adjacent angles formed by two
intersecting lines are supplementary.
Subtract 45° to isolate m4.
8-3 Line and Angle Relationships
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. In Exercise 28, line r || line s. Find the
measures of 4, 5, and 7.
55°, 125°, 125°