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**8-1 Similarity in Right Triangles**

One Key Term One Theorem Two Corollaries

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**Theorem 8-1 Altitude 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. C A B D

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Vocabulary Geometric Mean

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**#1 Finding the Geometric Mean**

Find the geometric mean of 15 and 20.

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Corollary 1 to Theorem 8-1 The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse. C A B D

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Corollary 2 to Theorem 8-1 The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse. C A B D

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#2 Solve for x and y. 4 12 x y 4 y x y 12 x 16

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

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

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