Mrs. McConaughy Geometry 1

Introduction to Proof:

During this lesson, we will: Identify angles as adjacent or vertical Identify supplementary and complementary angles and find their measures

Mrs. McConaughy Geometry 2

Introduction to Proof: Part I Types of Angles

Mrs. McConaughy Geometry 3

Review: Classifying Angles By Their Measures

Recall, the degree measure, m, of an angle must be 0 > m ≥ 180.

Angles can be classified into four categories by their measures:

Acute Obtuse Right Straight

Mrs. McConaughy Geometry 4

Classifying Angles By Their Position With Respect to Each

Other Adjacent angles :_________________

____________________________________________________________

two coplanar angles with a common side, a common vertex, and no common interior points

1 2

2 4 6 5 7

8

Which angles are adjacent to one another?

Mrs. McConaughy Geometry 5

Classifying Angles By Their Position With Respect to Each

OtherVertical angles: _________________

__________________________________________________________________________________________

nonadjacent angles formed by intersecting lines. Vertical angles share a common vertex and have sides which are opposite rays.Which angles form vertical angle pairs?

1

4 2 3 5

3 7 9

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Introduction to Proof: Part II Complementary &

Supplementary Angles

During this lesson, you will:identify supplementary and complementary anglesdetermine the measures of supplementary and complementary angles

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Definitions: Supplementary Definitions: Supplementary Angles and Linear PairsAngles and Linear Pairs

Two angles are supplementary if

the sum of their measures is 180 degrees. Each angle is called a supplement of the other.

If the angles are adjacent and supplementary, they are called a linear pair.

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Supplementary Angles and Supplementary Angles and Linear PairsLinear Pairs

m < 1 + m < 2 = 180 < 1 supplements < 2 < 1 is a supplement of < 2

m< PQS + m <SQR = 180< PQS and < SQR are a linear pair

Alert! Supplementary angles do not have to be adjacent. If they are adjacent, then the sides of the two angles which are not the common side form a straight angle.

1 2

m< GHJ + m <JHI = 180< GHJ and < JHI are a linear pair

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Example 1

Which are measures of supplementary angles?

30 ° and 160°103° and 67°86° and 94° 86° and 94° 180

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Definition: Complementary Definition: Complementary AnglesAngles

Complementary angles are related to right angles.

Definition: Complement

ary Angles

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

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Complementary AnglesComplementary AnglesComplementary angles do not have to be adjacent. If they are adjacent, then the sides of the two angles which are not the common side form a right angle.

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Example 2Example 2

Find the measure of a complement of each angle, if possible. Find the measure of a supplement.

Angle Measure

Complement

Supplement

60°

95°

m° 90 - m 180 - m

90 180

??

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Example 3Example 3

Find the measure of an angle if its measure is 60° more than its

supplement.

m = 180 – m + 60

Alert! We will use the m, 90 - m, and 180 – m to solve problems about angles.

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Example 4Example 4

Find the measure of an angle if its measure is twice that of its supplement.

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Example 5

Find the measure of an angle if its measure is 40 less than four times the measure of its complement.

measure is 40 less than four times the measure of its complement.

m = 4 (90 – m) - 40

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Final Checks for Understanding

Which are measures of complementary angles?…supplementary angles? ...neither?

1. 60° & 30°

2. 130° & 50°

3. 114° & 66° 4. 92° & 2°

5. 53° & 47°

6. 87° & 87°

7. 45° & 45°

8. 26° & 154°

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Final Checks for Understanding

What is the measure of a complement of each angle whose measure is given?1. 45° 2. 20° 3. 78° 4. 46° 5.

22.56. (m-

5)°

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Final Checks for Understanding

Translate words mathematical symbols

Complementary ___________________

Supplementary__________________

“a more than b”

_______________________

“a less than b”

_______________________

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Homework

Complementary & Supplementary Angles WS