Similar Right Triangles side lengths
Video, Interactive Applet and Examples
Video Tutorial on Similar Right Triangle
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)To better understand how the altitude of a right triangle acts as a mean proportion in similar triangles, look at the triangle below with sides a, b and c and altitude H.
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:
AD & BD
Find the sides that correspond with AC
AC & AB
AC & BC
Find the sides that correspond with BC
BC & AC
Example Problem Types
Students usually have to solve 2 different core types of problems involving the geometric mean.Problem Type #1) The altitude and hypotenuse
As you can see in the picture below, this problem type involves the altitude and 2 sides of the inner triangles ( these are just the two parts of the large outer triangle's hypotenuse) . This lets us set up a mean proportion involving the altitude and those two sides (see demonstration above if you need to be convinced that these are indeed corresponding sides of similar triangles .)
Problem Type #2) hypotenuse, Leg and Side
Involves the hypotenuse of the large outer triangle, one its legs and a side from one of the inner triangles.
Find the value of x in the triangle below: