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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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4-5

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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?

• 3. Given DEF and GHI, if D  G and E  H, why is F  I?

Objectives

TSW apply ASA, AAS, and HL to construct triangles and to solve problems.

TSW prove triangles congruent by using ASA, AAS, and HL.

Vocabulary

included side

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

Example 1: Applying ASA Congruence

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

Example 2

Determine if you can use ASA to prove NKL LMN. Explain.

### Proof Using Third Angle Theorem

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

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

Example 4

Use AAS to prove the triangles congruent.

Given:JL bisects KLM, K  M

Prove:JKL  JML

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.

Example 6: Applying HL Congruence

Example 7

Determine if you can use the HL Congruence Theorem to prove ABC  DCB. If not, tell what else you need to know.

Lesson Quiz: Part I

Identify the postulate or theorem that proves the triangles congruent.

Lesson Quiz: Part II

4. Given: FAB  GED, ABC   DCE, AC  EC

Prove: ABC  EDC

Statements

Reasons

Lesson Quiz: Part II Continued

Lesson Quiz: Part I

Identify the postulate or theorem that proves the triangles congruent.

HL

ASA

SAS or SSS

Lesson Quiz: Part II

4. Given: FAB  GED, ABC   DCE, AC  EC

Prove: ABC  EDC

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