1

Objectives

• Apply similarity relationships in right triangles to solve for missing lengths

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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

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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

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Solving Problems with Similar Right Triangles (2)

• Step 2: Set up a table with known valuesSmall leg Medium

legHypotenu

se

∆1 a b c

∆2 r h a

∆3 h s b• Step 3: Since all three triangles are similar, set up

a proportion and solve for a missing length.

Example: s

b

h

a

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Similar Right Triangles Example (1)

Step 3: Set up a proportion and solve for y.

Small leg

Medium leg

Hypotenuse

∆1 x 9

∆2 4 y x

∆3 y 5

x2 = 36

x = 6

x

x 9

4

Step 3: Set up a proportion and solve for x.

5

4 y

y

y2 = 20 = 4*5

y = 52

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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 leg

Medium leg

Hypotenuse

∆1 x 9

∆2 4 y x

∆3 y 5