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UNIT 4: CONGRUENT TRIANGLES 4.4 – Proving Triangles are Congruent: ASA and AAS MA30: GEOMETRY (Text Ref: Ch 4.4 Pg 220-227) Using the ASA & AAS Congruence Methods I. Using the ASA and AAS Congruence Methods A. Identifying the Included Side 1) Definition of Included Side Define & Identify Included Side 2) Identify the Included Side of the Triangles. (a) Postulate 21 Angle-Side-Angle Congruence Postulate Determine if ASA Congruence Postulate Applies Theorem 4.5 Angle-Angle-Side Congruence Theorem (b) (c) B. Postulate 21 – Angle-Side-Angle (ASA) Congruence Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. C. Determine whether the ASA Congruence Postulate can be used to prove the triangles are congruent. Explain. 1) 2) 3) D. Theorem 4.5 – Angle-Angle-Side Congruence Theorem If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent. 4.4 – Proving Triangles are Congruent: ASA and AAS (continued) Showing Triangles are Congruent Identifying Needed Congruences. E. Showing Triangles are Congruent Does the diagram give enough information to show that the triangles are congruent? If so, state the postulate or theorem you would use. Explain. 1) 2) Marking Tip 3) 4) Marking Tip 5) 6) Marking Tip F. State the third congruence that must be given to prove the two triangles are congruent using the indicated postulate or theorem. 1) ASA Congruence Postulate 2) AAS Congruence Theorem 3) ASA Congruence Postulate 4) AAS Congruence Theorem