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8.5 Proving Triangles are Similar Objectives: (1) The student will be able to use similarity theorems to prove that 2 triangles are similar. (2) The student will be able to similar triangles to solve real-life problems. Toolbox: Summary: Side-Side-Side (SSS) Similarity Theorem: If the lengths of the corresponding sides of 2 triangles are proportional, then the triangles are similar. Side-Angle-Side (SAS) Similarity Theorem: If one 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. Examples: 1. Write a paragraph proof. Given: ∆AEC ~ ∆GFH; DC = FH Prove: ∆BCD ~ ∆GHF 2. In the figure, AC= 6, AD = 10, BC = 9, and BE = 15. Describe how to prove that ∆ACB is similar to ∆DCE. 3. At an indoor climbing wall, a person whose eyes are 6 ft from the floor places a mirror 60 ft from the base of the wall. They then walk backwards 5 ft before seeing the top of the mirror. Use similar triangles to estimate the height of this wall. 4. Which of the following 3 triangles are similar?