1. Objective:Prove Angle Pair Relationships Prove Theorems- use properties, postulates, definitions and other proven theorems Prove: Right Angles Congruence Theorem If two angles are right angles, then they are congruent G: <1 & <2 are right angles Diagram: 1 2 P: StatementsReasons______________________ 1. <1 & <2 are right angles 1. Given 2. m<1=90, m<2=902. Def. of right angles 3. m<1 = m<23. Substitution 4. 4. Def. of congruence

2. G: C D P: A B StatementsReasons_____ 1. 1. Given 2. <B & <C are right angles2. Def. of perpendicular lines 3. 3. Right angles are congruent

3. Prove: Congruent Supplements Theorem If two angles are supplementary to the same angle (or to congruent angles), then they are congruent. G: <1 & <2 are supplementary anglesDiagram: 2 1 3 < 3 & <2 are supplementary angles P: StatementsReasons______________________ 1. <1 & <2 are supplementary angles 1. Given < 3 & <2 are supplementary angles 2. m<1+m<2=1802. Def. of supplementary angles m<3+m<2= 180 3. m<1+m<2 = m<3+m<23. Substitution 4. m<1=m<34. Subtraction (m<2) 5. 5. Def. of congruence

4. Congruence of Complements Theorem If two angles are complementary to the same angle(or to congruent angles), then they are congruent. Post 12 Linear Pair Postulate If two angles form a linear pair, then they are supplementary.

5. Prove:Vertical Angles Congruence Theorem If two angles are vertical angles then they are congruent. 7 G: <5 & <7 are vertical anglesDiagram: 5 6 P: Statements Reasons_________________ 1. <5 & <7 are vertical angles 1. Given 2. <5 & <6 are a linear pair2. Def. of linear pair <6 & <7 are a linear pair 3. <5 & < 6 are supplementary3. Linear pair postulate <6 & <7 are supplementary 4. 4. Congruent Supplements Thm