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Similar Right Triangles side lengths

Video, Interactive Applet and Examples

Video Tutorial

Geometric Mean example

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


In the proportion aboveon 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 aboveon the left, '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.

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Examples: 2 Types of Problems

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

Problem Type 1

The altitude and hypotenuse

As you can see in the picture below, this problem type involves the altitude and 2 sides of the inner triangles ( these are just the two parts of the large outer triangle's hypotenuse) . This lets us set up a mean proportion involving the altitude and those two sides (see demonstration above if you need to be convinced that these are indeed corresponding sides of similar triangles .)

general saas
What is the length of the altitude below?

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

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Problem Type 2. Hypotenuse, Leg and Side

Involves the hypotenuse of the large outer triangle, one its legs and a side from one of the inner triangles.

example 2 picture
Find the value of x in the triangle below:

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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Practice Problems

Back to Similar Triangles Next to Right Similar Triangle Applet