7.4 Similarity in Right Triangles

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Presentation transcript:

7.4 Similarity in Right Triangles

Theorem 7.3 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 B D A

Vocabulary Geometric mean - the number x such that , where a, b and x are positive numbers

Example Find the geometric mean of 4 and 18

Try it Find the geometric mean of 3 and 48

Corollary 1 to Theorem 7.3 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

Corollary 2 to Theorem 7.3 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

Solve for x and y x y 5 4

Answer Use Corollary 2 to solve for x Use corollary 1 to solve for y

Solve for x and y 4 x 12 y

Answer Use Corollary 2 to solve for x Use corollary 1 to solve for y

Classwork/Homework Pgs 394-395 #2-22 even, 26-36 even

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