Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL4-7 Triangle Congruence: ASA, AAS, and HL

Holt Geometry

Section 4.7Section 4.7

Holt McDougal Geometry

Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

Warm Up

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 McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

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 McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

Name the included side between each pair of angles.

1. R and K 2. X and R

3. 8 and 9 4. 10 and 12

5. 5 and 1 6. 4 and 2

Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

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

Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

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

Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

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

Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

State the postulate that you would use to prove the triangles congruent. Name the congruent triangles.

Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

State the postulate that you would use to prove the triangles congruent. Name the congruent triangles.

Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

Given: JL bisects KLM, K M

Prove: JKL JML

Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

What information is missing to say that:

a.ΔTUW ΔQOS by SAS b. ΔTUW ΔQOS by AAS

Holt McDougal Geometry

4-6 Triangle Congruence: ASA, AAS, and HL

Lesson Quiz: Part I

Identify the postulate or theorem that proves the triangles congruent.