Geometric Mean Worksheet
This worksheet focuses on understanding and applying the geometric mean in right triangles, including solving for missing side lengths and altitudes.
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Geometric Mean in Right Triangles
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Read each question carefully and solve for the missing values. Show all your work.
1. The geometric mean of two positive numbers a and b is .
2. In a right triangle, the altitude drawn to the hypotenuse creates three triangles.
3. The length of the altitude to the hypotenuse of a right triangle is the geometric mean between the two of the hypotenuse.
4. Find the value of x in the diagram below.
5. A right triangle has an altitude drawn to its hypotenuse, dividing it into segments of length 3 cm and 12 cm. What is the length of the altitude?
6. Find the value of y in the diagram below.
7. The hypotenuse of a right triangle is 20 units long. If one leg is 8 units long, and the adjacent segment of the hypotenuse is 4 units, find the length of the other leg using the geometric mean.
8. What is the geometric mean of 2 and 18?
6
10
12
36
9. The arithmetic mean and geometric mean of two distinct positive numbers are always equal.
True
False