# Exploring and Defining Geometric Mean (Leg)

- Author:
- Harrison Bosher, Tim Brzezinski

## Review from Last Class

Think about our exploration from last class. What did we learn about the three triangles shown in the module above? (If you don't remember, use the module to make some observations.)

Last class, we also discussed **geometric mean**. In your own words, define geometric mean.

What is the vocabulary word that we could use to describe segment CD?

## New Material

Compare to and finish the proportion.

What two values is AC the geometric mean of?

Look at the two values you answered in the previous question. Using the animation, describe how your two values relate to the hypotenuse of the original triangle.

What is a vocabulary word we could use to describe segment AC when relating it to the original triangle?

Compare to and finish the proportion.

What two values is BC the geometric mean of?

Look at the two values you answered in the previous question. Using the animation, describe how your two values relate to the hypotenuse of the original triangle.

What is a vocabulary word we could use to describe segment BC when relating it to the original triangle?

## Use the observations you made during this exploration to finish the theorem below.

In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the original triangle is the ________ _____ of the lengths of the _________ and the segment of the hypotenuse that is adjacent to the _____.

Type the value you found for AC below.

Type the value you found for MN below.