Prove Triangles Congruent by ASA & AAS

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Presentation transcript:

Prove Triangles Congruent by ASA & AAS Lesson 4.10 (M1) Use two more methods to prove triangle congruence

Vocabulary A flow proof uses arrows to show the flow of a logical argument. ASA Congruence Postulate: If two angles and the included side of one triangle are congruent to two angles of a second triangle, then the two triangles are congruent AAS Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.

ASA Congruence Postulate

AAS Congruence Theorem

GUIDED PRACTICE for Examples 1 and 2 In the diagram at the right, what postulate or theorem can you use to prove that RST VUT ? Explain. SOLUTION STATEMENTS REASONS Given S U Given RS UV The vertical angles are congruent RTS UTV

GUIDED PRACTICE for Examples 1 and 2 ANSWER Therefore are congruent because vertical angles are congruent so two pairs of angles and a pair of non included side are congruent. The triangle are congruent by AAS Congruence Theorem. RTS UTV

GUIDED PRACTICE for Examples 1 and 2 GIVEN ABC PROVE 3 = 180° 1 m 2 + STATEMENTS REASONS 1. Draw BD parallel to AC . Parallel Postulate 2. Angle Addition Postulate and definition of straight angle 4 m 2 5 + = 180° 3. Alternate Interior Angles Theorem 1 4 , 3 5 4. Definition of congruent angles 1 m = 4 3 5 , 5. Substitution Property of Equality 1 m 2 3 + = 180°