Question

corollary 1 to theorem 7-4:
the length of the ____________ to the hypotenuse of a __________ triangle is the geometric ____ of the lengths of the ____________ of the hypotenuse.

Explanation:

This is a key corollary in right triangle geometry, stating the relationship between the altitude to the hypotenuse and the segments it creates on the hypotenuse. The geometric mean of two numbers $a$ and $b$ is $\sqrt{ab}$, which applies here to the lengths of the hypotenuse segments and the altitude.

Answer:

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.