﻿ Similar Right Triangles formed by an Altitude. The Geometric Mean is the altitude of a right triangle.

# Similar Right Triangles side lengths

Video, Interactive Applet and Examples

### Video Tutorial

The mean proportion is any value that can be expressed just the way that 'x' is in the proportion on the above.

In the proportion above 'x', is the geometric mean, we could solve for x by cross multiplying and going from there (more on that later)

In the proportion above, '4', is the geometric mean

#### So what does this have to do with right similar triangles?

It turns out the when you drop an altitude (h in the picture below) from the the right angle of a right triangle, the length of the altitude becomes a geometric mean.
This occurs because you end up with similar triangles which have proportional sides and the altitude is the long leg of 1 triangle and the short leg of the other similar triangle .

Diagram 1

### Interactive Demonstration

To better understand how the altitude of a right triangle acts as a mean proportion in similar triangles, look at the triangle below with sides a, b and c and altitude H.

Drag Points And Click Button To Start

### Examples: 2 Types of Problems

Students usually have to solve 2 different core types of problems involving the geometric mean.

##### Problem Type 1

This problem is just example problem 1 above (solving for an altitude using the parts of the large hypotenuse)

##### Problem Type 2. Hypotenuse, Leg and Side

This problem is just example problem 2 because it involves the outer triangle's hypotenuse, leg and the side of an inner triangle.