Geometric Mean Worksheet
This worksheet focuses on understanding and applying the concept of geometric mean in various geometric contexts, including right triangles and similar figures.
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Geometric Mean Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. What is the geometric mean of two positive numbers, a and b? Explain in your own words.
2. Find the geometric mean of the following pairs of numbers. Round your answer to the nearest tenth if necessary.
a) 4 and 9:
b) 2 and 18:
c) 5 and 20:
d) 3 and 7:
3. In a right triangle, an altitude is drawn to the hypotenuse. Describe the relationships that involve the geometric mean.
4. Find the value of x in the diagram below.
5. In a right triangle, the altitude to the hypotenuse divides the hypotenuse into two segments. If the lengths of these segments are 5 and 20, what is the length of the altitude?
10
12
15
25
6. A right triangle has legs of length 6 and 8. Find the length of the altitude to the hypotenuse.