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Understanding Triangle Similarity: AA, SSS, and SAS Criteria

In this lesson, we explore triangle similarity through various criteria including AA, SSS, and SAS. We provide examples demonstrating how to prove triangles are similar and write similarity statements. Activities include verifying similarity for different triangle pairs and applying concepts to real-world problems, like measurements in engineering applications. This comprehensive presentation will help students grasp the fundamentals of triangle similarity, enhancing their geometric understanding and problem-solving skills.

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Understanding Triangle Similarity: AA, SSS, and SAS Criteria

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  1. Triangle Similarity: AA, SSS, and SAS 7-3 Warm Up Lesson Presentation Lesson Quiz Holt Geometry

  2. There are several ways to prove certain triangles are similar.

  3. Example 1: Using the AA Similarity Postulate Explain why the triangles are similar and write a similarity statement.

  4. Check It Out! Example 1 Explain why the triangles are similar and write a similarity statement.

  5. Example 2A: Verifying Triangle Similarity Verify that the triangles are similar. ∆PQR and ∆STU

  6. Example 2B: Verifying Triangle Similarity Verify that the triangles are similar. ∆DEF and ∆HJK

  7. Check It Out! Example 2 Verify that ∆TXU ~ ∆VXW.

  8. Example 3: Finding Lengths in Similar Triangles Explain why ∆ABE ~ ∆ACD, and then find CD.

  9. Check It Out! Example 3 Explain why ∆RSV ~ ∆RTU and then find RT.

  10. The photo shows a gable roof. AC || FG. ∆ABC ~ ∆FBG. Find BA to the nearest tenth of a foot. Example 5: Engineering Application

  11. You learned in Chapter 2 that the Reflexive, Symmetric, and Transitive Properties of Equality have corresponding properties of congruence. These properties also hold true for similarity of triangles.

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