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Proving Angle Relationships. Section 2-8. Protractor Postulate Given and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of , such that the measure of the angle formed is r. Angle Addition Postulate. I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
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1. Proving Angle Relationships Section 2-8

2. Protractor Postulate Given and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of , such that the measure of the angle formed is r.

3. Angle Addition Postulate If R is in the interior of , then Converse is also true. P R Q S

4. Supplement Theorem (2.3) • If 2 angle form a linear pair, then they are supplementary angles. 120 60

5. Complement Theorem (2.4) • If the noncommon sides of 2 adjacent angles form a right angle, then the angles are complementary angles.

6. Theorem 2-5 • Congruence of angles is reflexive, symmetric, and transitive.

7. Theorems 2-6 and 2-7 • Angles supplementary to the same angle or to congruent angles are congruent. • Angles complementary to the same angle or to congruent angles are congruent.

8. Theorems 2.8 - 2.13 • All right angles are congruent.(2.10) • Vertical angles are congruent.(2.8) • Perpendicular lines intersect to form 4 right angles. (2.9) 140 40 40 140

9. Perpendicular lines form congruent adjacent angles. (2.11) • If 2 angles are congruent and supplementary, then each angle is a right angle. (2.12) • If 2 congruent angles form a linear pair, then they are right angles.

10. Joke Time Why do bees have sticky hair? Because they have honeycombs!

11. What goes Oh, Oh, Oh? Santa walking backwards.