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Angle Pair Relationships. L.T. I can identify special angle pairs and use their relationships to find angle measure. A. Vertical Angles. 1. 2. 4. 3.

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angle pair relationships

Angle Pair Relationships

L.T. I can identify special angle pairs and use their relationships to find angle measure.

slide2

A. Vertical Angles

1

2

4

3

Previously, you learned that two angles are adjacent if they share a common vertex and side but have no common interior points. In this lesson, you will study other relationships between pairs of angles.

Two angles are vertical angles if their sides form two pairs of opposite rays.

Vertical Angle Pairs are CONGRUENT

2 and 4 are vertical angles.

1 and 3 are vertical angles.

slide3

B. Linear Pairs

5

6

Two adjacent angles are a linear pairif the form a straight line.

30°

150°

Linear Angle Pairs add up to 180°.

5 and 6 are a linear pair.

slide4

Identifying Vertical Angles and Linear Pairs

1

2

3

4

Answer the questions using the diagram.

Are 2 and 3 a linear pair?

SOLUTION

The angles are adjacent but their noncommon sides are not opposite rays.

No.

slide5

Identifying Vertical Angles and Linear Pairs

1

2

3

4

Answer the questions using the diagram.

Are 2 and 3 a linear pair?

Are 3 and 4 a linear pair?

SOLUTION

The angles are adjacent but their noncommon sides are not opposite rays.

No.

Yes.

The angles are adjacent and their noncommon sides are opposite rays.

slide6

Identifying Vertical Angles and Linear Pairs

1

2

3

4

Answer the questions using the diagram.

Are 2 and 3 a linear pair?

Are 3 and 4 a linear pair?

Are 1 and 3 vertical angles?

SOLUTION

The angles are adjacent but their noncommon sides are not opposite rays.

No.

Yes.

The angles are adjacent and their noncommon sides are opposite rays.

No.

The sides of the angles do not form two pairs of opposite rays.

slide7

Identifying Vertical Angles and Linear Pairs

1

2

3

4

Answer the questions using the diagram.

Are 2 and 3 a linear pair?

Are 3 and 4 a linear pair?

Are 1 and 3 vertical angles?

Are 2 and 4 vertical angles?

SOLUTION

The angles are adjacent but their noncommon sides are not opposite rays.

No.

Yes.

The angles are adjacent and their noncommon sides are opposite rays.

No.

The sides of the angles do not form two pairs of opposite rays.

The sides of the angles do not form two pairs of opposite rays.

No.

slide8

Finding Angle Measures

5

5

5

8

8

8

6

6

6

7

7

7

In the stair railing shown, 6 has a measure of 130˚. Find the measures of the other three angles.

SOLUTION

6 and 8 are vertical angles. So, they are congruent and have the same measure.

50°

m8 = m6 = 130˚

6 and 7 are a linear pair. So, the sum of their measures is 180˚.

130°

130°

130°

130°

m6 + m7 = 180˚

50°

130˚ + m7 = 180˚

m7 = 50˚

7and 5are vertical angles. So, they are congruent and have the same measure.

All 4 angles together equal 360°

slide9

C. Supplementary Angles

Definition: Two angles are supplementary if the sum of their measures is 180 degrees. Each angle is the supplement of the other.

1

2

These are supplements of each other because their angles add up to 180.

slide13

D. Complementary Angles

Definition: Two angles are complementary if the sum of their measures is 90 degrees. Each angle is the complement of the other.

1

2

These are complements of each other because their angles add up to be 90.

slide16

D. Angle Bisector

Definition: An angle bisector is a ray that divides an angle into two congruent angles. It cuts the angle in half.

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