Question

in the figure below, g is between e and h, and f is the midpoint of \\(\overline{eg}\\). if fh = 8 and fg = 2, find eh.\\(eh = \boxed{}\\)

Explanation:

Step1: Find FG and EG relationship

Since F is the midpoint of \( \overline{EG} \), \( EF = FG \). Given \( FG = 2 \), so \( EF = 2 \). Then \( EG=EF + FG=2 + 2 = 4 \).

Step2: Find EH using EG and GH

We know \( FH = 8 \), and \( FH=FG + GH \), so \( GH = FH - FG=8 - 2 = 6 \). Then \( EH=EG + GH = 4+6 = 12 \).

Answer:

\( 12 \)