__Geometric Mean__
- between two positive numbers a and b, is the positive number
x where a/b = x/b. Thus,

__Theorem__ - if
the altitudes drawn from the vertex of the right angle of a right
triangle to its hypotenuse, then the two triangles formed are
similar to thye given triangle and to each other

__Theorem__ - the
measure of the altitude drawn from the vertex of the right angle
of a right triangle to its hypotenuse is the geometric mean between
the measures of the two segments of the hypotenuse

__Theorem__ - if
the altitude is drawn to the hypotenuse of a right triangle, then
the measure of a leg of a triangle is the geometric mean between
the measures of the hypotenuse and the segment of the hypotenuse
adjacent to that leg

__Pythagorean Theorem__
- In a right triangle, the sum of the squares of the measures
of the legs equals the sqare of the measure of the hypotenuse

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