﻿ 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

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.