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

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Presentation Transcript
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4-5

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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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 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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Statements

Reasons

Lesson Quiz: Part II Continued

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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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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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