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Proving Triangle Similarity Theorems

Learn to prove triangles are similar using SSS and SAS Similarity Theorems, utilize properties of similar triangles, verify corresponding sides fit the same ratio, and understand Side-Side-Side and Side-Angle-Side Similarity.

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Proving Triangle Similarity Theorems

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  1. Lesson 8.5 Proving Triangles are Similar

  2. Lesson 8.5 Objectives • Prove triangles are similar using the SSS Similarity Theorem • Prove Triangles are similar using the SAS Similarity Theorem • Utilize properties of similar triangles

  3. 10 10 5 5 3 6 Theorem 8.2:Side-Side-Side Similarity • If the corresponding sides of two triangles are proportional, then the triangles are similar. • Your job is to verify that all corresponding sides fit the same exact ratio!

  4. 10 5 3 6 Theorem 8.3:Side-Angle-Side Similarity • If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar. • Your task is to verify that two sides fit the same exact ratio and the angles between those two sides are congruent!

  5. Using Theorems8.2 and 8.3 • These theorems share the abbreviations with those from proving triangles congruent in chapter 4. • SSS • SAS • So you now must be more specific • SSS Congruence • SSS Similarity • SAS Congruence • SAS Similarity • You chose based on what are you trying to show? • Congruence • Similarity

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