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Triangle Similarity Theorems Explained

Learn about Triangle Similarity Theorems: Angle-Angle (AA~), Side-Side-Side (SSS~), and Side-Angle-Side (SAS~). Understand when triangles are similar and how to prove it. Practice with example showing RST~PSQ.

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Triangle Similarity Theorems Explained

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  1. Z Warm Up W 12 7.5 U 5 V X Y 6 XYZ 5/6 10 9 100

  2. Proving Triangles Similar

  3. Angle-Angle (AA~) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. D A E F B C

  4. Side-Side-Side (SSS~) Similarity THM If the corresponding sides of two triangles are proportional, then the triangles are similar. D A E F B C

  5. Side-Angle-Side (SAS~) Similarity THM If the lengths of two sides are proportional and the included angle is congruent, then the triangles are similar D A F E B C

  6. Ex. Determine whether the triangles are similar. If so, tell which similarity test is used and complete the statement. Yes, AA~ M G 68° 43° 68° 43° H F L K V NO Y 7 3 Z 5 X W U 11

  7. S 5 4 Q P 12 15 R T Prove that RST~ PSQ 1. Two sides are proportional 2. Included angle is congruent SAS~

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