Objective:Prove Angle Pair Relationships Prove Theorems- use properties, postulates, definitions and other proven theorems Prove: Right Angles Congruence.

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Presentation transcript:

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 Def. of congruence

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

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: < 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= m<1+m<2 = m<3+m<23. Substitution 4. m<1=m<34. Subtraction (m<2) Def. of congruence

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.

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 Congruent Supplements Thm