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Geometry Lesson 2.8.notebook October 20, 2014 Proving Angle Relationships Protractor Postulate Given any angle, the measure can be put into a onetoone crrespondence with real numbers between 0 and 180. ANGLE ADDITION POSTULATE D is in the interior of if and only if Find if If and Find 1 Geometry Lesson 2.8.notebook October 20, 2014 SUPPLEMENT THEOREM If two angles form a linear pair, then they are supplementary angles. COMPLEMENT THEOREM If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary. form a linear pair. If 2 Geometry Lesson 2.8.notebook October 20, 2014 Properties of Angle Congruence Theorem Reflexive Property of Congruence Theorem Symmetric Property of Congruence Theorem Transitive Property of Congruence CONGRUENT SUPPLEMENT THEOREM Angles supplementary to the same angle or congruent angles are congruent. If Congruent Complement Theorems Angles complementary to the same or congruent angles are complementary. 3 Geometry Lesson 2.8.notebook October 20, 2014 GIVEN Angles 2 and 4 are vertical angles. Prove: are vertical angles. are nonadjcent angles formed by 2 interecting lines. form a linear pair. Definition of vertical angles Definition of a linear pair. form a linear pair. are supplementary Supplement Theorem are supplementary Congruent Supplement Theorem 4 Geometry Lesson 2.8.notebook October 20, 2014 VERTICAL ANGLE THEOREM If two angles are verical angles, then they are congruent. bisects Given: PROVE: bisects 5 Geometry Lesson 2.8.notebook October 20, 2014 Right Angle Theorems • • • • • Perpendicular lines intersect to form 4 right angles. All right angles are congruent. Perpendicular lines form congruent adjacent angles. If two angles are congruent and supplementary, then each angle is a right angle. If two congruent angles form a linear pair, then they are right angles. 6 Geometry Lesson 2.8.notebook October 20, 2014 P. 154 614 7