# 1 Objectives Apply similarity relationships in right triangles to solve for missing lengths.

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1 Objectives Apply similarity relationships in right triangles to solve for missing lengths

2 Right Triangle Similarity Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other

3 Solving Problems with Similar Right Triangles (1) Suppose one of the above letters is an unknown. Step 1: Redraw the original triangle into 3 separate triangles and label the triangles with given information

4 Solving Problems with Similar Right Triangles (2) Step 2: Set up a table with known values Small legMedium legHypotenuse 1abc 2rha 3hsb Step 3: Since all three triangles are similar, set up a proportion and solve for a missing length. Example:

5 Similar Right Triangles Example (1) Step 3: Set up a proportion and solve for y. Small leg Medium leg Hypotenuse 1x9 24yx 3y5 x 2 = 36 x = 6 Step 3: Set up a proportion and solve for x. y 2 = 20 = 4*5 y =

6 Similar Right Triangles Example (2) Solve for x and y. Step1: Redraw into 3 separate triangles; label. Step2: Fill in the table with known information Small legMedium legHypotenuse 1x9 24yx 3y5

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