Section 8-1 Similarity in Right Triangles. Geometric Mean If a, b, and x are positive numbers and Then x is the geometric mean. x and x are the means.

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Section 8-1 Similarity in Right Triangles

Geometric Mean If a, b, and x are positive numbers and Then x is the geometric mean. x and x are the means a and b are the extremes

Example: Find the geometric mean between 5 and Set up a proportion: 2. Cross Multiply: 3. Solve: *Simplify the radical if possible!

Theorem 8-1 If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

A NB C

Corollary 1 When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse.

A NB C

Corollary 2 When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg.

A NB C So we can say: or