7.4 Similarity in Right Triangles

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Presentation transcript:

7.4 Similarity in Right Triangles 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.

Geometric Mean The geometric mean of two positive numbers a and b is the positive number x that satisfies

Find a Geometric Mean Find the geometric mean of 6 and 15.

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 hypotenuse and the length of the segment of the hypotenuse adjacent to the leg.

Using the Corollaries What are the values of x and y?

More Practice!!!!! Homework – Textbook p. 464 – 465 #3 – 6, 9 – 21.