2. $overline{fg}$ is the geometric mean of which two segments?
$overline{ef}$ and $overline{fh}$
$overline{hg}$ and $overline{eh}$
$overline{eg}$ and $overline{eh}$
$overline{eg}$ and $overline{gh}$

Question

Accepted Answer

# Brief Explanations:
To determine which two segments $ \overline{FG} $ is the geometric mean of, we recall the geometric mean theorem (or altitude-on-hypotenuse theorem) in right triangles. If we assume a right triangle with an altitude drawn to the hypotenuse, the altitude is the geometric mean of the segments it divides the hypotenuse into.

Looking at the options, we analyze the relationships:
- For $ \overline{FG} $ to be the geometric mean of two segments, say $ a $ and $ b $, we need $ FG^2 = a \times b $.
- The correct relationship from the geometric mean theorem (altitude in right triangle) is that the altitude (here $ \overline{FG} $) to the hypotenuse ($ \overline{EH} $) of a right triangle divides the hypotenuse into segments $ \overline{EG} $ and $ \overline{GH} $, and the altitude is the geometric mean of these two segments. So $ FG^2 = EG \times GH $, meaning $ \overline{FG} $ is the geometric mean of $ \overline{EG} $ and $ \overline{GH} $.

# Answer:
D. $ \overline{EG} $ and $ \overline{GH} $ (assuming the last option is labeled D; if the original options have labels, use the correct label with the segments $ \overline{EG} $ and $ \overline{GH} $)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Answer: