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7-3 Angle Relationships
Warm Up
Problem of the Day
Lesson Presentation
Course 2
7-3 Angle Relationships
Warm Up
Find the complement of each angle
measure.
1. 30° 60°
2. 42° 48°
Find the supplement of each angle
measure.
3. 150°
Course 2
30°
4. 82° 98°
7-3 Angle Relationships
Problem of the Day
Draw three points that are not on the
same line. Label them A, B, and C. How
many lines can you draw that are
determined by the points? Name the
lines.
3; AB, AC, BC
Course 2
7-3 Angle Relationships
Learn to identify parallel, perpendicular,
and skew lines, and angles formed by a
transversal.
Course 2
7-3 Angle
InsertRelationships
Lesson Title Here
Vocabulary
perpendicular lines
parallel lines
skew lines
adjacent angles
vertical angles
transversal
corresponding angles
Course 2
7-3 Angle Relationships
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 Angle Relationships
Reading Math
The symbol means “is parallel to.” The
symbol means “is perpendicular to.”
Course 2
7-3 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
Course 2
The lines appear to intersect
to form right angles.
7-3 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.
Course 2
The lines are in different
planes and do not intersect.
7-3 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
Course 2
The lines are in the same
plane and do not intersect.
7-3 Angle Relationships
Check It Out: Example 1A
Tell whether the lines appear parallel,
perpendicular, or skew.
WX and XU
WX  XU
Course 2
The lines appear to intersect
to form right angles.
7-3 Angle Relationships
Check It Out: Example 1B
Tell whether the lines appear parallel,
perpendicular, or skew.
WX and UV
WX and UV
are skew
Course 2
The lines are in different
planes and do not intersect.
7-3 Angle Relationships
Check It Out: Example 1C
Tell whether the lines appear parallel,
perpendicular, or skew.
WX and ZY
WX || ZY
Course 2
The lines are in the same
plane and do not intersect.
7-3 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. 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 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.
Course 2
7-3 Angle Relationships
A transversal is a line that
intersects two or more lines. Line
t is a transversal. When the lines
that are intersected are parallel,
four pairs of corresponding
angles are formed.
Corresponding angles are on
the same side of the transversal
and are both above or both below
the parallel lines. Angles 1 and 5
are corresponding angles.
Corresponding angles are
congruent.
Course 2
7-3 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°.
Course 2
7-3 Angle Relationships
Additional Example 2B: Using Angle Relationships to
Find Angle Measures
Line n
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°.
Course 2
7-3 Angle Relationships
Additional Example 2C: Using Angle Relationships to
Find Angle Measures
Line n
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°.
Course 2
7-3 Angle Relationships
Check It Out: Example 2A
Line n
line p. Find the measure of the angle.
45° 4
5 6
2 3 135° 7
3
n
p
3 and the 45° angle are vertical angles. Since
vertical angles are congruent, m3 = 45°.
Course 2
7-3 Angle Relationships
Check It Out: Example 2B
Line n
line p. Find the measure of the angle.
45° 4
5 6
2 3 135° 7
n
p
6
6 and the 135° angle are obtuse angles.
Since vertical angles are congruent, m6 =
135°.
Course 2
7-3 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
4 is an obtuse angle.
m4 + 45° = 180°
–45°
–45°
m4 = 135°
Course 2
p
In the figure, the acute and obtuse
angles are supplementary.
Subtract 45° to isolate m4.
7-3 Angle
InsertRelationships
Lesson Title Here
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
of 4, 5, and 6.
55°, 125°, 125°
Course 2
line 5. Find the measure