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Geometric Mean

Similar Right Triangles

If you drop a perpendicular from the right angle of a right triangle to the opposite side, you will create three similar right triangles. This altitude is known as the geometric mean.
    Geometric Mean example The geometric mean is any 'b' that can be expressed as
    in a proportion.

    To better understand how the altitude of a right triangle acts as a geometric mean 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.
Diagram of Geomoetric mean
Find the corresponding sides:
 Answer 

AD &

AD & Find the sides that correspond with AC
 Answer 

AC &

AC &
Find the sides that correspond with BC
 Answer 

BC &

BC &


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