1. 2.8 Proving Angle Relationships

2. New Postulates

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. New Theorems

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

7. Theorems 2.6 and 2.7

8. Example 3
In the figure, 1 and 4 form a linear pair, and m3+m4=180º. Prove that 3 and 4 are congruent.
Given: 1 and 4
form a linear pair
Prove: 3 ≅ 4

9. In the figure, 1 and 4 form a linear pair, and m3+m4=180º
In the figure, 1 and 4 form a linear pair, and m3+m4=180º. Prove that 3 and 4 are congruent.
Statements
Reasons 1.
1. Given
2. 1 and 4 form a linear pair. 2. 3. 4.
4. Definition of supplementary angles
5. 3≅4 5.

10. Vertical Angles Theorem

11. Example 4
If 1 and 2 are vertical angles and m1 = d – 32 and m2 = 175 – 2d, find m1 and m2. Justify each step.

12. If 1 and 2 are vertical angles and m1 = d – 32 and m2 = 175 – 2d, find m1 and m2. Justify each step.
Statements
Reasons 1.
1. Given
2. 1  2 2.
3. m1 = m2 3. 4.
4.Substitution
5. 3d – 32 = 175 5. 6.
6. Addition Property
7. 3d=207 7. 8.
8.Substitution

13. Right Angle Theorems