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