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Chapter 4, Lesson 5 Objective: Date: Students will learn to prove triangles are congruent using the SSS, SAS, ASA, AAS, and HL Postulates Wups Identify the congruent triangles in each figure (i.e., write a congruence statement). 1. 2. A. Proving Triangles Congruence Goal: Prove two Triangles are Congruent. o How many parts are there in a triangle? o To do this, we just have to show three ‘strategic’ pairs of corresponding parts are congruent o We will show 5 methods for doing this. 1. Side – Side – Side Method Definition SSS Side – Side – Side Three pairs of corresponding sides are congruent. 1 Representation Method Definition SAS Side – Angle – Side Two pairs of corresponding sides and the INCLUDED angle are congruent ASA Angle – Side – Angle Two pairs of corresponding angles and the INCLUDED side is congruent. AAS Angle – Angle – Side Two pairs of corresponding angles and a corresponding side is congruent. HL Hypotenuse – Leg Two right triangles are congruent if their hypotenuse and a pair of legs are respectively congruent. Representation You cannot prove triangles congruent by AAA or SSA! Here’s why… You can’t use AAA because: http://www.mathopenref.com/congruentaaa.html You can’t use ASS because: http://www.mathopenref.com/congruentssa.html Here’s a way to remember … Side-Side-Angle (SSA) can be reversed to get Angle-Side-Side (ASS!) Don’t say ASS! Don’t use ASS! It’s NOT a congruence property!!! Don’t use SSA either, because it’s just ASS backwards!! 2 B. Examples: State whether each pair of triangles is congruent by SSS, SAS, ASA, AAS, or HL. If not method exists, state None. Determine if the triangle are congruent. If so, state how you know and give a triangle congruence statement. 10. 11. 12. 13. 3