Question

Is my answer correct??

Answer 1

Answer: Last option.

Step-by-step explanation:

For this exercise it is important to remember that a Right triangle is a triangle that has an angle that measures 90 degrees.

By definition, given a Right triangle, if you draw an altitutde from the vertex of the angle that measures 90 degrees (The right angle) to the hypotenuse, the measure of that altitude is the geometric mean between the measures of the two segments of the hypotenuse.

In this case, you have the Right triangle $EFH$  given in the picture attached.

You can notice that $FG$ goes from the vertex of right angle ($\angle F=90\°$ ) to the hypotenuse $EH$. Therefore, it divides the hypotenuse into two segments. These are:

$EG$ and $GH$

Therefore, $FG$ is the geometric mean of the segments $EG$ and $GH$.