Question

in the figure below, g is between e and h, and f is the midpoint of eg. if eh = 8 and fg = 2, find gh.
gh = □

Explanation:

Step1: Find the length of \(EG\)

Since \(F\) is the mid - point of \(EG\), then \(EG = 2FG\). Given \(FG = 2\), so \(EG=2\times2 = 4\).

Step2: Use the segment addition postulate

By the segment addition postulate, \(EH=EG + GH\). We know \(EH = 8\) and \(EG = 4\). Substitute the values into the formula: \(8=4 + GH\).

Step3: Solve for \(GH\)

Subtract 4 from both sides of the equation \(8 = 4+GH\). So \(GH=8 - 4\).

Answer:

\(4\)