4-5
This presentation is the property of its rightful owner.
Sponsored Links
1 / 22

4-5 PowerPoint PPT Presentation


  • 46 Views
  • Uploaded on
  • Presentation posted in: General

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 ?

Download Presentation

4-5

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


4 5

4-5

Triangle Congruence: ASA, AAS, and HL

Holt Geometry

Warm Up

Lesson Presentation

Lesson Quiz


4 5

  • 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?


4 5

Objectives

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

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


4 5

Vocabulary

included side


4 5

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


4 5

Example 1: Applying ASA Congruence

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


4 5

Example 2

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


Proof using third angle theorem

Proof Using Third Angle Theorem


4 5

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


4 5

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


4 5

Example 4

Use AAS to prove the triangles congruent.

Given:JL bisects KLM, K  M

Prove:JKL  JML


4 5

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.


4 5

Example 6: Applying HL Congruence


4 5

Example 7

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


4 5

Lesson Quiz: Part I

Identify the postulate or theorem that proves the triangles congruent.


4 5

Lesson Quiz: Part II

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

Prove: ABC  EDC


4 5

Statements

Reasons

Lesson Quiz: Part II Continued


4 5

Lesson Quiz: Part I

Identify the postulate or theorem that proves the triangles congruent.

HL

ASA

SAS or SSS


4 5

Lesson Quiz: Part II

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

Prove: ABC  EDC


4 5

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


  • Login