﻿ 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 Tutorialon Similar Right Triangle

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

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

In the proportion on the left, '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 (left side) and the short leg of the other similar triangle (right side in pic below)

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.

Below is a picture of the many similar triangles created when you drop the altitude from a right angle of a right triangle.

AB
BD
AB
BC
AB
AC

### Example Problem Types

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

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

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

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