holt geometry 4-5 triangle congruence: asa and aas 4-5 triangle congruence: asa and aas holt...

Holt Geometry

4-5 Triangle Congruence: ASA and AAS4-5 Triangle Congruence: ASA and AAS

Holt Geometry

Warm Up

Lesson Presentation

Lesson Quiz

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

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?

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

• Apply ASA and AAS to construct triangles and to solve problems.

• Prove triangles congruent by using ASA and AAS.

Objectives

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

included side

Vocabulary

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

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

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

Example 1: Applying ASA Congruence

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

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

Example 2

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

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

Holt Geometry

4-5 Triangle Congruence: ASA and 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

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

Lesson Quiz: Part I

Identify the postulate or theorem that proves the triangles congruent, or determine “not possible.”

ASA

not possible

SAS or SSS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

Congruence Postulates Extra Examples

SSS, ASA, SAS, AAS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

1. Given: ÐA @ÐDAB @ DEÐB @ ÐE.

ASA

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

2. Given: ÐC @ÐFÐB @ ÐE

AC @ DF.

AAS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

3. Given: ÐC @ÐF

ÐB @ ÐE

BC @ EF.

ASA

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

4. Given: ÐC @ÐF

AC @ DF

BC @ EF.

SAS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

5. Given: ÐA @ÐD

ÐC @ ÐF

BC @ EF.

AAS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

6. Given: AB @ DE

BC @ EF

AC @ DF.

SSS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

7. Given: ÐC and ÐF are rt. Ðs AB @ DE

ÐA @ ÐD.

AAS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

8. Given: ÐC and ÐF are rt. Ðs AC @ DF

ÐB @ ÐE.

AAS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

9. Given: ÐC @ÐF

ÐB @ ÐE

AC @ DF.

AAS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

10. Given: ÐC and ÐF are rt. Ðs

ÐB @ ÐE

BC @ EF.

ASA

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

11. Given: ÐA @ÐD

AB @ DE

ÐB @ ÐE.

ASA

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

12. Given: ÐA @ÐD

ÐC @ ÐF

BC @ EF.

AAS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

13. Given: BC ^ AC

EF ^ DF

AB @ DE

ÐB @ ÐE.

AAS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

14. Given: AB @ DE

BC @ EF

AC @ DF.SSS

Holt Geometry

4-5 Triangle Congruence: ASA and AAS

15. Given: ÐC @ÐF

AC @ DF

BC @ EF.SAS