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Triangle Similarity: Proofs and Problem Solving

Learn how to prove triangles are similar using AA, SSS, and SAS criteria, and apply similarity concepts to solve problems. Explore examples and step-by-step explanations for verifying similarity and finding lengths in similar triangles.

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Triangle Similarity: Proofs and Problem Solving

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  1. Objectives Prove certain triangles are similar by using AA, SSS, and SAS. Use triangle similarity to solve problems.

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

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

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

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

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

  7. Example 3A: Finding Lengths in Similar Triangles Explain why ∆ABE ~ ∆ACD, and then find CD. Step 1 Prove triangles are similar.

  8. Example 3A Continued Step 2 Find CD.

  9. Check It Out! Example 3B Explain why ∆RSV ~ ∆RTU and then find RT. Step 1 Prove triangles are similar.

  10. Check It Out! Example 3B Continued Step 2 Find RT.

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