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

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Do Now 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?

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL TSW apply ASA, AAS, and HL to construct triangles and to solve problems. TSW prove triangles congruent by using ASA, AAS, and HL. Objectives

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL included side Vocabulary

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Example 1: Applying ASA Congruence Determine if you can use ASA to prove the triangles congruent. Explain.

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Example 2 Determine if you can use ASA to prove NKL LMN. Explain.

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Proof Using Third Angle Theorem

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL You can use the Third Angles Theorem to prove another congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Example 3: Using AAS to Prove Triangles Congruent Use AAS to prove the triangles congruent. Given: X V, YZW YWZ, XY VY Prove: XYZ VYW

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Example 4 Use AAS to prove the triangles congruent. Given: JL bisects KLM, K M Prove: JKL JML

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Example 5: Applying HL Congruence Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know.

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Example 6: Applying HL Congruence

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Example 7 Determine if you can use the HL Congruence Theorem to prove ABC DCB. If not, tell what else you need to know.

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Lesson Quiz: Part I Identify the postulate or theorem that proves the triangles congruent.

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Lesson Quiz: Part II 4. Given: FAB GED, ABC DCE, AC EC Prove: ABC EDC

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Lesson Quiz: Part II Continued ReasonsStatements

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Lesson Quiz: Part I Identify the postulate or theorem that proves the triangles congruent. ASA HL SAS or SSS

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Lesson Quiz: Part II 4. Given: FAB GED, ABC DCE, AC EC Prove: ABC EDC

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Holt Geometry 4-5 Triangle Congruence: ASA, AAS, and HL Lesson Quiz: Part II Continued 5. ASA Steps 3,4 5. ABC EDC 4. Given 4. ACB DCE; AC EC 3. Supp. Thm.3. BAC DEC 2. Def. of supp. s 2. BAC is a supp. of FAB; DEC is a supp. of GED. 1. Given 1. FAB GED ReasonsStatements

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