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4-5. 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 ?.
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4-5 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
2. Given: ÐC @ÐFÐB @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