Question

point f is on line segment \\(\overline{eg}\\). given \\(ef = 6\\) and \\(fg = 8\\), 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 \( EF = 6 \) and \( FG = 8 \), so substitute these into the formula: \( EG = 6 + 8 \).

Step3: Calculate the sum

\( 6 + 8 = 14 \).

Answer:

The length of \( \overline{EG} \) is \( 14 \).