Section 4-3 Triangle Congruence (ASA, AAS) SPI 32C: determine congruence or similarity between triangles SPI 32M: justify triangle congruence given a diagram.

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Presentation transcript:

Section 4-3 Triangle Congruence (ASA, AAS) SPI 32C: determine congruence or similarity between triangles SPI 32M: justify triangle congruence given a diagram Objectives: Prove 2 triangles are  using AAS and ASA postulate Postulates and Theorems to show Congruence SSS: Side-Side-Side SAS: Side-Angle-Side ASA: Angle-Side-Angle AAS: Angle-Angle-Side HL: Hypotenuse-Leg (right triangle only)

Angle-Side-Angle (ASA) Postulate Postulate 4-3 Angle-Side-Angle (ASA) Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Using ASA Postulate Write a paragraph proof (write proof in complete sentences) Given: Prove: Proof:  ABC   AED because all right angles are congruent. You are given that. Therefore, by ASA.

Angle-Angle-Side (AAS) Theorem Theorem 4-2 Angle-Angle-Side (AAS) Theorem If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non- included side of another triangle, then the triangles are congruent.

StatementReason Given Alternate Interior Angles Given Def Segment Bisector Using the AAS Theorem Write a two column proof that uses AAS Given: || Prove: || AAS Theorem

Write a two-column proof that uses AAS. Given:  B  D, AB || CD Prove: ABC CDA StatementsReasons 1.  B  D, AB || CD1. Given 4. ABC CDA4. AAS Theorem 2.  BAC  DCA2. If lines are ||, then alternate interior angles are. 3. AC CA3. Reflexive Property of Congruence Write two-column proof for AAS