Similar Right Triangle TheoremsSimilar Right Triangle Theorems

Theorem 8.17 – If the altitude is Theorem 8.17 – If the altitude is drawn to the hypotenuse if a right drawn to the hypotenuse if a right triangle, then the two triangles triangle, then the two triangles formed are similar to the original formed are similar to the original triangle and to each other.triangle and to each other.

Geometric Mean Geometric Mean If a, x, and b are positive andIf a, x, and b are positive and

aa = = xx

xx b b

Then Then xx is called the is called the geometric meangeometric mean between between aa and and bb. The geometric mean . The geometric mean is always positive.is always positive.

Geometric Mean TheoremGeometric Mean Theorem

Theorem 8.16 – If the altitude is Theorem 8.16 – If the altitude is drawn to the hypotenuse of a right drawn to the hypotenuse of a right triangle, then the measure of the triangle, then the measure of the altitude is the geometric mean altitude is the geometric mean between the measures of the parts between the measures of the parts of the hypotenuse.of the hypotenuse.