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Geometry

Learn how to prove congruence of triangles using the AAS and HL theorems, and explore different ways to prove overlapping triangles congruent. Includes examples and practice problems.

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Geometry

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  1. Geometry 4.5 Other Methods of Proving Triangles Congruent

  2. 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.

  3. 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. B Y ABC XYZ C Z A X

  4. Right Triangle Vocabulary Remember the definition of a right triangle It has one right angle LEG HYPOTENUSE LEG

  5. 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. A X ABC XYZ Z B C Y

  6. Summary of Ways to Prove Triangles Congruent Right triangles All triangles SSS Post SAS Post ASA Post AAS Thm HL Thm

  7. OVERLAPPING TRIANGLES Given: <2 <3 L P <1 <4 Q 1 4 2 3 M N Name the congruence 1 2 3 4 ∆ LMN congruent to ∆ PNM by ASA same side

  8. B A C D 1. Given: Prove:

  9. Given: • Prove: J K 2 1 A B

  10. 4. Given:Angles M and R are right angles • Prove: S T M R

  11. 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.

  12. Let’s do a few from the homework Turn to pg. 142 CE #5, #6 , #10 Now pg. 143 WE #2

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