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Understanding Triangle Congruence: A Comprehensive Guide

This guide covers essential triangle congruence theorems including AAS (Angle-Angle-Side) and HL (Hypotenuse-Leg) for right triangles. It explains how to identify congruence using various methods such as SSS, SAS, ASA, AAS, and HL, with practical examples. The text emphasizes recognizing overlapping triangles and that the hypotenuse is opposite the right angle. Engage in exercises to enhance understanding of triangle proofs. Complete classroom and written assignments to practice these concepts and gain recognition in class.

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Understanding Triangle Congruence: A Comprehensive Guide

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  1. Answers to Homework • All answers to SELF TESTS are in the back!!! • Questions???

  2. 4-5 Other Methods of Proving triangles Congruent

  3. Theorem • AAS • Angle-Angle-Side: If two angles and a NON-INCLUDED side are cong., then the triangles are cong. • HL (90) • Hypotenuse-Leg: If the hypotenuse and leg of two RIGHT triangles are cong, then the triangles are cong.

  4. Right Triangles HL: Must have the Hyp and EITHER Leg How do you know which side is the Hypotenuse? It’s across from the 90. Always the longest. Usually the “diagonal”. leg Hypt. leg

  5. TOO: PAGE 142 #10-12 • Name the congruent triangles • Choose from SSS, SAS, ASA, AAS, HL • These Are OVERLAPPING Triangles, watch me do the first one.

  6. #10 ∆ABC and ∆DCB by SSS BC is a shared side Look at the Given info B A E D C

  7. #11 ∆LMN and ∆PNM by ASA P L Q 1 4 2 3 M N

  8. #12 ∆UWY and ∆VZX by HL U V W Z X Y

  9. TOO: same page #1 and 2: There are 2 answers for each! Do these both on your whiteboard. I will pick the best to show to the class!! And you will get a prize!!

  10. Homework • Page 142 #3-9 Classroom Exercises • Page 143 #1-7 Written Exercises • #2 is 6 steps • #3 is 5 Steps • #4 is 4 Steps

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