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4.4 ASA & AAS Congruence HMWK: p. 223, #s 8-18 All, 19-24, 29, 30 Game Plan: Today I will be able to 1. Prove s using ASA and AAS 2. Apply s to real world problems 3. Use constructions to copy s Warm-up: If SSS represents side-side-side and SAS represents side-angle-side , describe the meaning of the following. 1. AAA 2. AAS 3. SSA 4. ASA 4.4 ASA & AAS Congruence Triangle Congruence Angle Side Angle (ASA) Congruence Postulate: If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. 1. Sketch a diagram of this postulate. 2. Think – Pair – Share … explain why this postulate is true. 4.4 ASA & AAS Congruence Triangle Congruence Angle Angle Side (AAS) Congruence Theorem: If two angles and the nonincluded side of a triangle are congruent to two angles and the nonincluded side of another triangle, then the triangles are congruent. 1. Sketch a diagram of this postulate. 2. Think – Pair – Share … explain why this postulate is true. Be sure to explain why we must have at least one pair of sides congruent. 4.4 ASA & AAS Congruence Proving Congruent Ex 1: Is it possible to prove the following triangles congruent? 4.4 ASA & AAS Congruence Proving Congruent 4.4 ASA & AAS Congruence Applying Congruent Triangles Ex 3: When searching for a missing airplane, searchers used observations from people in two different areas of a city. As shown, the observers were able to describe sight lines A from observers in different houses. One sightline was from observers in House A and the other sightline was fro observers in House B. Assuming the sightlines are accurate, did the searchers have enough information to locate the airplane? B C Hint: Think about what information we know about the triangle …angles? sides? 4.4 ASA & AAS Congruence Copying a Triangle • • • • • • Need construction tools Draw a triangle (relatively large). Label the triangle ABC Draw a line and label the line m Follow along together. Draw another triangle and switch with a partner to copy. 4.4 ASA & AAS Congruence Wrap -up What information do you need to know in order to apply the 1) ASA postulate, and 2) AAS theorem? Tomorrow … 1. More on proving triangles congruent 2. Looking at a quiz on Wednesday or Thursday … a proof quiz. 3. Remember projects are due on Wednesday!!!