9.1

Question 1

Theorem 9.1

Answer 1

If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original (biggest) triangle and to each other.

Question 2

Theorem 9.2

Answer 2

In a right triangle, the length of the altitude from the right triangle to the hypotenuse is the geometric mean of the lengths of the two segments.

Question 3

Theorem 9.3

Answer 3

In a right triangle, the altitude from the right triangle to the hypotenuse divides the hypotenuse into two segments. Each leg of the (biggest/original) right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

Question 4

Geometric Mean

Answer 4

The geometric mean of two numbers, a and b is the positive number x such that a/x=x/b.