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4-5. Triangle Congruence: ASA, AAS, and HL. Holt Geometry. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Geometry. AC. Warm Up 1. What are sides AC and BC called? Side AB ? 2. Which side is in between  A and  C ?

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4-5

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  1. 4-5 Triangle Congruence: ASA, AAS, and HL Holt Geometry Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry

  2. AC • Warm Up • 1.What are sides AC and BC called? Side AB? • 2. Which side is in between A and C? • 3. Given DEF and GHI, if D  G and E  H, why is F  I? legs; hypotenuse Third s Thm.

  3. Objectives Quick review: SSS and SAS are triangle congruence tests Prove triangles congruent by using ASA, AAS, and HL.

  4. Vocabulary included side and included angle

  5. Review: We already know that SSS is a test for triangle congruence.

  6. An included angle is an angle formed by two adjacent sides of a polygon. B is the included angle between sides AB and BC.

  7. It is given that BA BD and ABC  DBC. By the Reflexive Property of , BC  BC. So ∆ABC  ∆DBC by SAS. Check It Out! Example 2 Use SAS to explain why ∆ABC  ∆DBC.

  8. An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.

  9. Example 2: Applying ASA Congruence Determine if you can use ASA to prove the triangles congruent. Explain. Two congruent angle pairs are give, but the included sides are not given as congruent. Therefore ASA cannot be used to prove the triangles congruent.

  10. By the Alternate Interior Angles Theorem. KLN  MNL. NL  LN by the Reflexive Property. No other congruence relationships can be determined, so ASA cannot be applied. Check It Out! Example 2 Determine if you can use ASA to prove NKL LMN. Explain.

  11. You can use the Third Angles Theorem to prove another congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

  12. Check It Out! Example 3 Use AAS to prove the triangles congruent. Given:JL bisects KLM, K  M Prove:JKL  JML

  13. Lesson Quiz: Part I Identify the postulate or theorem that proves the triangles congruent. HL ASA SAS or SSS

  14. Lesson Quiz: Part II 4. Given: FAB  GED, ABC   DCE, AC  EC Prove: ABC  EDC

  15. Statements Reasons 1. FAB  GED 1. Given 2. BAC is a supp. of FAB; DEC is a supp. of GED. 2. Def. of supp. s 3. BAC  DEC 3.  Supp. Thm. 4. ACB  DCE; AC  EC 4. Given 5. ABC  EDC 5. ASA Steps 3,4 Lesson Quiz: Part II Continued

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