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Proving Angle Relationships Section 2-8

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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.

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

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

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

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

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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.

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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

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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.

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

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

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