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Exploring Triangle Congruence: Mastering ASA and AAS Theorems

Dive into the world of triangle congruence with this comprehensive lesson focused on the Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) postulates. Engage in dynamic learning through warm-up questions, examples, and quizzes that will help you construct and prove triangle congruence effectively. Understand the concept of included sides and explore various congruence scenarios with interactive exercises. This lesson aims to deepen your understanding of geometric principles and enhance problem-solving skills in triangle congruence.

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Exploring Triangle Congruence: Mastering ASA and AAS Theorems

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  1. 4-5 Triangle Congruence: ASA and AAS Holt Geometry Warm Up Lesson Presentation Lesson Quiz

  2. 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?

  3. Objectives • Apply ASA and AAS to construct triangles and to solve problems. • Prove triangles congruent by using ASA and AAS.

  4. Vocabulary included side

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

  6. Example 1: Applying ASA Congruence Determine if you can use ASA to prove the triangles congruent. Explain.

  7. Example 2 Determine if you can use ASA to prove NKL LMN. Explain.

  8. 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

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

  10. Congruence Postulates Extra Examples SSS, ASA, SAS, AAS

  11. 1. Given: ÐA @ÐD AB @ DEÐB @ÐE. ASA

  12. 2. Given: ÐC @ÐFÐB @ÐE AC @ DF. AAS

  13. 3. Given: ÐC @ÐF ÐB @ÐE BC @ EF. ASA

  14. 4. Given: ÐC @ÐF AC @ DF BC @ EF. SAS

  15. 5. Given: ÐA @ÐD ÐC @ÐF BC @ EF. AAS

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

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

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

  19. 9. Given: ÐC @ÐF ÐB @ÐE AC @ DF. AAS

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

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

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

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

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

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

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