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8.3 Methods of Proving Triangles Similar

Objectives: Prove triangles similar by AA, SSS, SAS. 8.3 Methods of Proving Triangles Similar. Angle-Angle-Angle Similarity Postulate (AAA~). If the 3 angles of one triangle are congruent to 3 angles of another triangle, then the triangles are similar. P. A. Q. R. B. C.

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8.3 Methods of Proving Triangles Similar

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  1. Objectives: • Prove triangles similar by AA, SSS, SAS 8.3 Methods of Proving Triangles Similar

  2. Angle-Angle-Angle Similarity Postulate (AAA~) If the 3 angles of one triangle are congruent to 3 angles of another triangle, then the triangles are similar. P A Q R B C

  3. Angle-Angle Similarity (AA~) Theorem 62: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. P A Q R B C

  4. Side-Side-Side Similarity Theorem (SSS~) Theorem 63: If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar. P A Q R B C

  5. Example 1: Which triangles are similar? ∆ABC ~ ∆MNO – by SSS ~ M A P 5 25 15 3 6 10 R Q 7 O 18 N C B 30 What is the scale factor? 5 : 3

  6. Side-Angle-Side Similarity Theorem (SAS~) Theorem 64: If the lengths of 2 sets of corresponding sides of two triangles are proportional, and the included angles are congruent, then the triangles are similar. P A Q R B C

  7. Example 2: If AC = 6, AD = 10, BC = 9, BE = 15, is ∆ACB~ ∆DCE? Yes, by SAS ~ A E C D B What is the scale factor? 3 : 2

  8. Example 3: If AC = 18, CE = 9, IK = 18, DI = 36, mC= mI= 98°, are the triangles similar? A K I C E D What is the scale factor? What is the similarity statement?

  9. Example 4: Are these triangles similar? If yes, what is the scale factor? XYZ: XY = 5, YZ = 4, mZ= 50° UVW: UV = 10, VW = 8, mW= 50°

  10. C D Example 5: Given: ABCD is a parallelogram Prove: ∆BFE ~ ∆CFD F E A B • DFC BFE • Vertical Angles • Definition of parallelogram • Alternate Interior Angles • CDF E AA ~ Theorem ∆BFE ~ ∆CFD

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