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Geometry 4.5 Other Methods of Proving Triangles Congruent B A We have 2 congruent angles and one congruent side………but the side is not the included side. Can anything be proved? In Chapter 3 you were introduced to this corollary: if 2 angles of one triangle are congruent to 2 angles of another triangle, then the 3rd angles are congruent. This would allow us to conclude that angles A and B are congruent, and would create an ASA congruence. So the moral to the story is: any two congruent angles and one congruent side gives you congruent triangles. The AAS (Angle-Angle-Side) Theorem If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. ABC B XYZ C A X Y Z Right Triangle Vocabulary Remember the definition of a right triangle LEG It has one right angle HYPOTENUSE LEG The HL (Hypotenuse - Leg) Theorem If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. ABC A X XYZ B C Y Z Summary of Ways to Prove Triangles Congruent All triangles SSS Post SAS Post ASA Post AAS Thm Right triangles HL Thm <3 <1 <4 Given: <2 OVERLAPPING TRIANGLES L P Q 1 Name the congruence 2 M 1 ∆ LMN congruent to ∆ PNM by ASA same side 4 3 N 2 3 4 1. Given: B B D BC || AD Prove: DC AB A C D 3. Given: JAB KBA J 1 2 Prove: K J K 1 A 2 B 4. Given: Angles M and R are right angles SR TM Prove: S T M R SMR TRM Homework pg. 142 CE #1-13 WE # 1-8 Bring Compass Just a reminder of what’s allowed in the bins: EMPTY plastic bottles, aluminum cans, and paper. Whats NOT allowed: wrappers, gum, Ziploc baggies, half-empty beverages. If these items are in the bins, then the whole bin gets dumped into the trash. Last week, I spent the first 5 minutes of each class demonstrating what goes in each receptacle. Since this small demonstration, my students have been very good about proper placement of waste items in my classroom. Let’s do a few from the homework Turn to pg. 142 CE #5, #6 , #10 Now pg. 143 WE #2