FG is the geometric mean of EG and GH by using the Right triangle altitude theorem.
Important information:
- The given figure of a triangle EFH.
Right triangle altitude theorem:
According to the Right triangle altitude theorem, if an altitude is drawn on the hypotenuse of a right triangle, then the altitude of a right triangle is the geometric mean of the two segments of the hypotenuse.
From the given figure it is clear that,
- Triangle EFH is a right triangle because angle F is a right angle.
- FG is the altitude on the hypotenuse.
- Two segments of the hypotenuse are EG and GH.
Using the Right triangle altitude theorem, we get FG is the geometric mean of EG and GH.
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