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Geometric Means:
The geometric mean between two numbers x and z is defined as
x/y = y/z
and y is called the geometric mean of x and z.
Theorem:
If the altitude is drawn to the hypotenuse of a right triangle,
then the two triangles formed are similar to each other and to
the original triangle.
Corollary 1:
When the altitude is drawn to the hypotenuse of the right
triangle, the length of the altitude is the geometric mean
between the new segments of the hypotenuse.
Corollary 2:
When the altitude is drawn to the hypotenuse of the right
triangle, each leg is the geometric mean between the whole
hypotenuse and the segment of the whole hypotenuse that is adjacent
to that leg.
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