 # Lesson 2.6 p. 109 Proving Statements about Angles Goal: to begin two-column proofs about congruent angles.

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Lesson 2.6 p. 109 Proving Statements about Angles Goal: to begin two-column proofs about congruent angles

Properties of Angle Congruence Theorem 2.2 Reflexive: Transitive : Symmetric:

Two-Column Proof Using Transitive Property Given:Prove: Statements Reasons 8 4 1 7 3 2 6 5

Theorem 2.3 Right Angle Congruence Theorem All right angles are congruent.

Theorem 2.4 Congruent Supplements Theorem If two angles are supplementary to the same angle (or to congruent angles), then they are congruent. 1 3 2

Theorem 2.5 Congruent Complements Theorem If two angles are complementary to the same angle (or to congruent angles), then they are congruent. 4 56

Theorem 2.6 Vertical Angles Theorem Vertical angles are congruent. 1 4 3 2

Postulate 12 Linear Pair Postulate If two angles form a linear pair, then they are supplementary. 12

Given: Prove: Statements Reasons 1 3 2

Definitions you should know! Perpendicular lines Right angle Supplementary angles Complementary angles Segment bisector Angle bisector Linear pair Vertical angles Also, review Segment Addition Postulate & Angle Addition Postulate