Question

in the figure below, g is between e and h, and f is the midpoint of \overline{eg}. if fh = 6 and fg = 2, find eh.

eh = \square

Explanation:

Step1: Find the length of \( EG \)

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

Step2: Find the length of \( GH \)

We know that \( GH=FH - FG \). Given \( FH = 6 \) and \( FG = 2 \), so \( GH=6 - 2=4 \).

Step3: Calculate the length of \( EH \)

By the segment - addition postulate \( EH=EG + GH \). Substitute \( EG = 4 \) and \( GH = 4 \) into the formula, we get \( EH=4+4 = 8 \).

Answer:

\( 8 \)