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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

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.



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 congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

Use AAS to prove the triangles congruent.

Given:X  V, YZW  YWZ, XY  VY

Prove: XYZ  VYW


Example 4 congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

Use AAS to prove the triangles congruent.

Given:JL bisects KLM, K  M

Prove:JKL  JML


Example 5: Applying HL Congruence congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

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 congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).


Example 7 congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

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 congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

Identify the postulate or theorem that proves the triangles congruent.


Lesson Quiz: Part II congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

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

Prove: ABC  EDC


Statements congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

Reasons

Lesson Quiz: Part II Continued


Lesson Quiz: Part I congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

Identify the postulate or theorem that proves the triangles congruent.

HL

ASA

SAS or SSS


Lesson Quiz: Part II congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

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

Prove: ABC  EDC


Statements congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

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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