4-5 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: ASA and AAS 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 Apply ASA and AAS to construct triangles and to solve problems. Prove triangles congruent by using ASA and AAS.

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.

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

Lesson Quiz: Part I Identify the postulate or theorem that proves the triangles congruent, or determine “not possible.” ASA not possible SAS or SSS

Congruence Postulates Extra Examples SSS, ASA, SAS, AAS

1. Given: ÐA @ÐD AB @ DE ÐB @ ÐE. ASA

2. Given: ÐC @ÐF ÐB @ ÐE AC @ DF. AAS

3. Given: ÐC @ÐF ÐB @ ÐE BC @ EF. ASA

4. Given: ÐC @ÐF AC @ DF BC @ EF. SAS

5. Given: ÐA @ÐD ÐC @ ÐF BC @ EF. AAS

6. Given: AB @ DE BC @ EF AC @ DF. SSS

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

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

9. Given: ÐC @ÐF ÐB @ ÐE AC @ DF. AAS

10. Given: ÐC and ÐF are rt. Ðs ÐB @ ÐE BC @ EF. ASA

11. Given: ÐA @ÐD AB @ DE ÐB @ ÐE. ASA

12. Given: ÐA @ÐD ÐC @ ÐF BC @ EF. AAS

13. Given: BC ^ AC EF ^ DF AB @ DE ÐB @ ÐE. AAS

14. Given: AB @ DE BC @ EF AC @ DF. SSS

15. Given: ÐC @ÐF AC @ DF BC @ EF. SAS