Question

point f is on line segment (overline{eg}). given (fg = 5) and (ef = 14), determine the length (overline{eg}).

Explanation:

Step1: Recall segment addition postulate

If a point \( F \) is on segment \( \overline{EG} \), then \( EG = EF + FG \).

Step2: Substitute given values

We know \( EF = 14 \) and \( FG = 5 \), so substitute these into the formula: \( EG = 14 + 5 \).

Step3: Calculate the sum

\( 14 + 5 = 19 \).

Answer:

The length of \( \overline{EG} \) is \( 19 \).