Geometric Mean of Right Triangles
Name
You are given a right triangle and are asked to construct the altitude. This yields three similar
right triangles.
1.
What are the three similar right triangles?
2.
What is the hypotenuse of each of the three triangles? What is the long leg of each
triangle? What is the short leg of each triangle?
Long Leg
Short Leg
Hypotenuse
Triangle 1
Triangle 2
Triangle 3
You find the ratio of the long leg to the short leg in all three similar triangles.
3.
Give a statement of equality (something = something else) that includes the measure of
the altitude on both sides of the “=” sign.
4.
Give two more proportions that each contain a same measurement on both sides.
A geometric mean between two numbers a and b is the positive number x where
a x
 . This
x b
can be translated to “x is the geometric mean between a and b.”
5.
Translate the three proportions you created in this fashion. (Ex, WX is the geometric
mean of XY and YZ.)
Tab two contains a figure with AZ = 8 and BZ = 4. Find the following:
a. AB
b. ZC
c. BC
d. CA