Geometric Mean

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.

Find the corresponding sides:
 Answer 

AD & AB

AD & BD

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Find the sides that correspond with AC
 Answer 

AC & DB

AC & DC

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Find the sides that correspond with BC
 Answer 

AC & BC
AC & AB