on Similar Right Triangle
The mean proportion is any value that can be expressed just the way that 'x' is in the proportion on the left.
n the proportion on the left 'x', is the geometric mean, we could solve for x by cross multiplying and going from there (more on that later)
In the proportion on the left, '4', is the geometric mean
So what does this have to do with right similar triangles?
It turns out the when you drop an altitude (h in the picture below) from the the right angle of a right triangle, the length of the altitude becomes a geometric mean.
This occurs because you end up with similar triangles which have proportional sides and the altitude is the long leg of 1 triangle (left side) and the short leg of the other similar triangle (right side in pic below)
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:
Find the sides that correspond with AC
Find the sides that correspond with BC
Example Problem Types
Students usually have to solve 2 different core types of problems involving the geometric mean.