 # 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.

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

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

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

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

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.

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) 40 140

 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.

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

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

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