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Triangle Similarity Theorems: SSS and SAS Explained

Understand Side-Side-Side (SSS) and Side-Angle-Side (SAS) similarity theorems to prove triangles are similar. Learn how to establish ratios and identify proportional sides. Discover three ways to prove triangle similarity.

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Triangle Similarity Theorems: SSS and SAS Explained

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  1. Section 8-5 Proving Triangles are Similar

  2. Side-side-side Similarity theorem(sss theorem) • If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

  3. If K L Y Z J X then

  4. In order to see if sides are proportional to tell if triangles are similar: • Pair off the shortest sides then the longest sides then the remaining sides. • See if all of the ratios are the same • Be sure to reduce!

  5. Side-angle-side Similarity theorem(sas theorem) • 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.

  6. K If L Y Z J X then

  7. In summary, there are 3 ways to prove triangles similar: • AA ~ Postulate • SSS ~ Theorem • SAS ~ Theorem

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