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Geometry Triangle Congruence by ASA and AAS Notes Objective: To prove two triangles congruent using ASA and AAS Previously, we learned that two triangles are congruent if all three sides are congruent ( ) and if two sides and an included angle are congruent ( ) for each triangle. We have two more ‘shortcuts’ to learn about triangle congruency. Angle-Side-Angle Postulate (ASA) If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then Example 1: Use the 3 triangles below for parts A and B. A) Which triangle is congruent to CAT by the ASA Postulate? (Recall: When you write a congruence statement remember to list corresponding vertices in the same order.) B) Can you conclude that INF is congruent to either of the other two triangles? Explain. Example 2: Can you conclude if the two triangles below are congruent by the ASA Postulate? If so, write a congruence statement. If not, explain why. Example 3: If J is the midpoint of WB , can you conclude the triangles below are congruent by ASA? Angle-Angle-Side Theorem (AAS) 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 Example 4: Explain why these two triangles are congruent by AAS. Then write a congruence statement. Example 5: Given that XQ || TR and that XR bisects QT , show that the two triangles below are congruent by AAS. Then write a congruence statement. Example 6: Complete the proof. Given: PQ || RS Prove: PQR SRQ Statements PQ || RS Justifications Alternate interior angles Alternate interior angles Reflexive Property PQR SRQ Example 7: What else would you need to know for the two triangles to be congruent by a) ASA b) AAS c) Write a congruence statement for the two triangles.