Download Holt CA Course 1

8-3 Angle Relationships
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
8-3 Angle Relationships
Warm Up
Complete each sentence.
1. Angles whose measures have a sum of 90° are
_______________
.
complementary
2. A part of a line that starts at one point and
ray
extends forever in one direction is called a _______.
3. Angles whose measures have a sum of 180° are
supplementary
______________.
4. A part of a line between two points is called a
segment
____________.
Holt CA Course 1
8-3 Angle Relationships
California
Standards
Review of Grade 6
MG2.2 Use properties of
complementary and supplementary angles and
the sum of the angles of a triangle to solve
problems involving an unknown angle.
Also covered: 6MG2.1
Holt CA Course 1
8-3 Angle Relationships
Additional Example 1: Finding Angle Measures
Use the diagram to find each angle
measure.
A. If m1 = 37°, find m 3.
1 and 2 are supplementary.
m2 = 180° – 37° = 143°
The measures of 2 and 3 are supplementary.
m3 = 180° – 143° = 37°
So m1 = m3, or 1  3.
Holt CA Course 1
8-3 Angle Relationships
Writing Math
~ which is read as
The symbol for congruence is =,
“is congruent to.”
Holt CA Course 1
8-3 Angle Relationships
Additional Example 1: Finding Angle Measures
Use the diagram to find each angle measure.
B. If m4 = y°, find m2.
3 and 4 are supplementary.
m3 = 180° – y°
2 and 3 are supplementary.
m2 = 180° – m3
o – yo
Substitute
180
= 180° – (180o – yo) for m3.
= 180° – 180° + y° Distributive Property
= y°
Simplify.
So m4 = m2, or 4  2.
Holt CA Course 1
8-3 Angle Relationships
Check It Out! Example 1
Use the diagram to find each angle measure.
2
A. If m1 = 42°, find m3.
1
3
4
The measures of 1 and 2 are supplementary.
m2 = 180° – 42° = 138°
The measures of 2 and 3 are supplementary.
m3 = 180° – 138° = 42°
So m1 = m3, or 1  3.
Holt CA Course 1
8-3 Angle Relationships
Check It Out! Example 1
Use the diagram to find each angle measure.
B. If m4 = x°, find m2.
3 and 4 are supplementary.
m3 = 180° – x°
2 and 3 are supplementary.
2
1
3
4
m2 = 180° – m3
o – xo
Substitute
180
= 180° – (180o – xo) for m3.
= 180° – 180° + x° Distributive Property
= x°
Simplify.
So m4 = m2, or 4  2.
Holt CA Course 1
8-3 Angle Relationships
The angles in Example 1 are examples of
adjacent angles and vertical angles. These
angles have special relationships because
of their positions.
Adjacent angles have a common vertex
and a common side, but no common
interior points.
Vertical angles are the nonadjacent
angles formed by two intersecting lines.
Holt CA Course 1
8-3 Angle Relationships
A transversal is a line that intersects two
or more lines that lie in the same plane.
Transversals to parallel lines form angle
pairs with special properties.
Holt CA Course 1
8-3 Angle Relationships
Holt CA Course 1
8-3 Angle Relationships
Additional Example 2: Finding Angle Measures
of Parallel Lines Cut by Transversals
In the figure, line
of the angle.
l || line m. Find the measure
A. 4
Corresponding angles are congruent.
m4 = 124°
Holt CA Course 1
8-3 Angle Relationships
Additional Example 2: Finding Angle Measures
of Parallel Lines Cut by Transversals
In the figure, line
of the angle.
l || line m. Find the measure
B. 2
2 is supplementary to the 124° angle.
m2 + 124° = 180°
–124°
m2
Holt CA Course 1
–124° Subtract.
= 56° Simplify.
8-3 Angle Relationships
Additional Example 2: Finding Angle Measures
of Parallel Lines Cut by Transversals
In the figure, line
of the angle.
C. 6
l || line m. Find the measure
2 and 6 are corresponding angles.
m6 = 56°
Holt CA Course 1
8-3 Angle Relationships
Check It Out! Example 2
In the figure, line
of the angle.
A. 7
l || line m. Find the measure
Alternate exterior angles are congruent.
m7 = 144°
1
Holt CA Course 1
144°
3 4
5 6
7 8
m
n
8-3 Angle Relationships
Check It Out! Example 2
In the figure, line
of the angle.
B. 1
l || line m. Find the measure
1 is supplementary to the 144° angle.
m1 + 144° = 180°
–144° –144°
m 1
= 36°
Holt CA Course 1
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144°
3 4
5 6
7 8
m
n
8-3 Angle Relationships
Check It Out! Example 2
In the figure, line
of the angle.
l || line m. Find the measure
C. 6
Corresponding angles
are congruent.
m6 = 144°
Holt CA Course 1
1
144°
3 4
5 6
7 8
m
n
8-3 Angle Relationships
Lesson Quiz
In the figure, line a || line b.
1. Name all angles congruent to 3.
1, 5, 7
2. Name all the angles supplementary to 6.
1, 3, 5, 7
3. If m1 = 105° what is m3?
105°
4. If m5 = 120° what is m2?
60°
Holt CA Course 1