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Transcript
June 30, 2013 Geometry 2-8 Proving Angle Relationships Postulate 2.10: Protractor Postulate: Given any angle, the measure can be assigned a value between 0 and 180. Postulate 2.11: Angle Addition Postulate: Point D is in the interior of ⦛ABC if and only if m⦛ABD + m ⦛DBC = m⦛ ABC. D A B 6 7 C ⦛6 and ⦛7 form a linear pair. If m⦛ 6 = 3x + 32 and m ⦛7 = 5x + 12, find m ⦛6 and m⦛ 7. 3x + 32 + 5x + 12 = 180 8x + 44 = 180 8x = 136 x = 17 m⦛6 = 3(17) + 32 = 83 m⦛7 = 5(17) + 12 = 97 A B 1 2 3 C Find m⦛3 if m⦛1 = 23 and m⦛ABC = 131. m⦛1 + m ⦛ 2 + m ⦛3 = m⦛ABC 23 + 90 + m ⦛3 = 131 m ⦛3 = 18 Theorem 2.3: Supplement Theorem: If two angles form a linear pair, then they are supplementary angles. Theorem 2.4: Complement Theorem: If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles. Theorem 2.5: Properties of Angle Congruence: Congruence of angles is reflexive, symmetric, and transitive. Our next two theorems are closely related. Theorem 2.6: Congruent Supplements Theorem: Angles that are supplementary to the same angle or to congruent angles are congruent. Theorem 2.7: Congruent Complements Theorem: Angles that are complementary to the same angle or to congruent angles are congruent. Theorem 2.8: Vertical Angles Theorem: If two angles are vertical angles, then they are congruent. Theorem 2.11: Perpendicular lines form congruent adjacent angles. We will close out this lesson with a few theorems that pertain only to right angles. Theorem 2.12: If two angles are congruent and supplementary, then both angles are right angles. Theorem 2.9: Perpendicular lines intersect to form 4 right angles. Theorem 2.10: All right angles are congruent. Theorem 2.13: If two congruent angles form a linear pair, then they are right angles.