holt ca course 1 8-3 angle relationships warm up warm up california standards california standards...
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Holt CA Course 1
8-3 Angle Relationships
Warm Up
California StandardsCalifornia Standards
Lesson Presentation
PreviewPreview
Holt CA Course 1
8-3 Angle RelationshipsWarm UpComplete each sentence.
1. Angles whose measures have a sum of 90° are _______________ .
2. A part of a line that starts at one point and extends forever in one direction is called a _______.
3. Angles whose measures have a sum of 180° are ______________.
4. A part of a line between two points is called a ____________.
complementary
ray
supplementary
segment
Holt CA Course 1
8-3 Angle Relationships
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
California Standards
Holt CA Course 1
8-3 Angle RelationshipsAdditional Example 1: Finding Angle Measures
Use the diagram to find each angle measure.
A. If m1 = 37°, find m3.
1 and 2 are supplementary.
The measures of 2 and 3 are supplementary.
m2 = 180° – 37° = 143°
m3 = 180° – 143° = 37°
So m1 = m3, or 1 3.
Holt CA Course 1
8-3 Angle Relationships
The symbol for congruence is =, which is read as “is congruent to.”
Writing Math ~
Holt CA Course 1
8-3 Angle Relationships
B. If m4 = y°, find m2.
m3 = 180° – y°
m2 = 180° – m3
= 180° – 180° + y°
= y°
Substitute 180o – yo for m3.
So m4 = m2, or 4 2.
Additional Example 1: Finding Angle Measures
Use the diagram to find each angle measure.
3 and 4 are supplementary.
2 and 3 are supplementary.
= 180° – (180o – yo)
Distributive Property
Simplify.
Holt CA Course 1
8-3 Angle Relationships
A. If m1 = 42°, find m3.1
23
4
Check It Out! Example 1
The measures of 1 and 2 are supplementary.
The measures of 2 and 3 are supplementary.
m2 = 180° – 42° = 138°
m3 = 180° – 138° = 42°
So m1 = m3, or 1 3.
Use the diagram to find each angle measure.
Holt CA Course 1
8-3 Angle Relationships
m3 = 180° – x°
m2 = 180° – m3
= 180° – 180° + x°
= x°
Substitute 180o – xo for m3.
So m4 = m2, or 4 2.
Check It Out! Example 1Use the diagram to find each angle measure.
3 and 4 are supplementary.
2 and 3 are supplementary.
= 180° – (180o – xo)
Distributive Property
Simplify.
B. If m4 = x°, find m2.
1
23
4
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
In the figure, line l || line m. Find the measure of the angle.
Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals
A.4
m4 = 124°
Corresponding angles are congruent.
Holt CA Course 1
8-3 Angle Relationships
B.2
m2 + 124° = 180°
2 is supplementary to the 124° angle.
m2 = 56°
–124° –124° Subtract.
Simplify.
In the figure, line l || line m. Find the measure of the angle.
Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals
Holt CA Course 1
8-3 Angle Relationships
2 and 6 are corresponding angles.C6
m6 = 56°
In the figure, line l || line m. Find the measure of the angle.
Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals
Holt CA Course 1
8-3 Angle Relationships
Check It Out! Example 2
A.7
m7 = 144°
1 144°3 4
5 67 8
m
n
In the figure, line l || line m. Find the measure of the angle.
Alternate exterior angles are congruent.
Holt CA Course 1
8-3 Angle Relationships
B.1
m1 + 144° = 180°
1 is supplementary to the 144° angle.
m1 = 36°–144° –144° 1 144°
3 45 6
7 8
m
n
Check It Out! Example 2
In the figure, line l || line m. Find the measure of the angle.
Holt CA Course 1
8-3 Angle Relationships
C.6
m6 = 144°1 144°
3 45 6
7 8
m
n
Check It Out! Example 2
In the figure, line l || line m. Find the measure of the angle.
Corresponding angles are congruent.
Holt CA Course 1
8-3 Angle RelationshipsLesson Quiz
In the figure, line a || line b.
1. Name all angles congruent to 3.
2. Name all the angles supplementary to 6.
3. If m1 = 105° what is m3?
4. If m5 = 120° what is m2?
1, 5, 7
1, 3, 5, 7
105°
60°