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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