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Proving Triangle Similarity Using SSS and SAS Theorems

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Dive into the concepts of triangle similarity through the Side-Side-Side (SSS) and Side-Angle-Side (SAS) theorems. Learn to determine if triangles are similar by verifying proportions and corresponding angles. This lesson covers essential objectives such as proving triangles ∆PQR and ∆STU are similar and finding dimensions like CD for triangles ∆ABE and ∆ACD. Engage with real-life applications, such as constructing a lean-to shelter while ensuring similarity in design. Follow examples to strengthen your understanding of these foundational geometry principles.

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Proving Triangle Similarity Using SSS and SAS Theorems

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  1. 6.5: Prove Triangles similar by SSS and SAS Objectives: Prove triangles similar by using SSS and SAS similarity theorems. Use SSS or SAS to solve triangle proportions. Common Core Standards: G-SRT-4, G-SRT-5, G-MG-3

  2. Verify that the triangles are similar. ∆PQR and ∆STU

  3. Verify that the triangles are similar. ∆DEF and ∆HJK

  4. Verify that ∆TXU ~ ∆VXW.

  5. Explain why ∆ABE ~ ∆ACD, and then find CD.

  6. Is either DEF or GHJsimilar to ABC? EXAMPLE 1

  7. Find the value of xthat makes ABC ~ DEF. EXAMPLE 2

  8. Lean-to Shelter You are building a lean-to shelter starting from a tree branch, as shown. Can you construct the right end so it is similar to the left end using the angle measure and lengths shown? EXAMPLE 3

  9. Tell what method you would use to show that the triangles are similar. EXAMPLE 4

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