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**4-5 Warm Up Lesson Presentation Lesson Quiz**

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

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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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Objectives TSW apply ASA, AAS, and HL to construct triangles and to solve problems. TSW prove triangles congruent by using ASA, AAS, and HL.

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Vocabulary included side

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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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**Example 1: Applying ASA Congruence**

Determine if you can use ASA to prove the triangles congruent. Explain.

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Example 2 Determine if you can use ASA to prove NKL LMN. Explain.

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**Proof Using Third Angle Theorem**

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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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**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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Example 4 Use AAS to prove the triangles congruent. Given: JL bisects KLM, K M Prove: JKL JML

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**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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**Example 6: Applying HL Congruence**

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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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Lesson Quiz: Part I Identify the postulate or theorem that proves the triangles congruent.

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**Lesson Quiz: Part II 4. Given: FAB GED, ABC DCE, AC EC**

Prove: ABC EDC

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**Lesson Quiz: Part II Continued**

Reasons Statements

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

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**Lesson Quiz: Part II 4. Given: FAB GED, ABC DCE, AC EC**

Prove: ABC EDC

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**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 Reasons Statements

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4.4 Proving Triangles are Congruent: ASA and AAS Geometry.

4.4 Proving Triangles are Congruent: ASA and AAS Geometry.

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