1. Section 2.8: Proving Angle Relationships

2. Angle Addition Postulate
VOCAB
Vocabulary
Definition
Picture
Angle Addition Postulate

3. Example 1:
CONSTRUCTION Using a protractor, a construction worker measures that the angle a beam makes with a ceiling is 42°. What is the measure of the angle the beam makes with the wall?

4. VOCAB Vocabulary Definition Picture Supplement Theorem
Supplement Theorem
Complement Theorem

5. Example 2:
TIME At 4 o’clock, the angle between the hour and minute hands of a clock is 120º. When the second hand bisects the angle between the hour and minute hands, what are the measures of the angles between the minute and second hands and between the second and hour hands?

6. Properties of Angle Congruence
VOCAB
Properties of Angle Congruence
Reflexive Property of Congruence
Symmetric Property of Congruence
Transitive Property of Congruence

7. VOCAB Vocabulary Definition Picture Congruent Supplement Theorem
Congruent Supplement Theorem
Congruent Complement Theorem

9. Example 3:
In the figure, Ð1 and Ð4 form a linear pair, and mÐ3 + mÐ1 = 180°.
Prove that Ð3 and Ð4 are congruent.
Statements
Reasons 1.
2. Angle 1 and Angle 4 form a linear pair
3. Angle 1 and Angle 4 are supplementary 4. 5.
1. Given 2. 3.
4. Def. of Supplementary Angles

10. Vertical Angles Theorem
VOCAB
Vocabulary
Definition
Picture
Vertical Angles Theorem

11. Example 4:

12. VOCAB Right Angle Theorems Theorem Definition Picture 2.9 2.10 2.11
2.9
2.10
2.11
2.12
2.13

13. Summary