Similar Right Triangles

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Presentation transcript:

Similar Right Triangles Section 9-1 Similar Right Triangles

Theorem 9-1 If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle.

A B C D CBD ACD CBD

In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments.

Theorem 9-2 The length of the altitude is the geometric mean of the lengths of the two segments.

A B C D AD DB

Theorem 9-3 The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

AD AB C B A D Part that is from the little triangle Part that is from the big triangle

BD BA C B A D Part that is from the little triangle Part that is from the big triangle