The first formula is BIG triangle over MEDIUM trianlge, and the last step that you get is the geometric mean, which is usually the first number from the BIG triangle.
The next formula is BIG triangle over SMALL triangle, in which the geometric mean would be the SECOND number that you get from the BIG triangle, and the THIRD number that you get from the SMALL triangle.
The last formula is MEDIUM triangle over SMALL triangle, in which the geometric mean is the SECOND number that you get from the MEDIUM triangle, and the FIRST number that you get from the SMALL triangle.
Theorem: If an altitude is drawn to the hypotenuse of a right triangle, then the two triangles that are formed are similar to the original.
Example
Find the geometric mean of 8 and 16.
8/x=x/16 x squared =the square root of 128.
x=the square root of 128, then break it down.
when broken down, the square root of 128=8 square root 2.