Question

in the figure below, g is between e and h, and f is the midpoint of (overline{eg}). if (fg = 5) and (fh = 9), find (eh)

Explanation:

Step1: Find the length of \(EG\)

Since \(F\) is the mid - point of \(EG\), by the definition of a mid - point \(EF = FG\). Given \(FG = 5\), then \(EF=FG = 5\), and \(EG=EF + FG=5 + 5=10\).

Step2: Find the length of \(GH\)

We know that \(FH = 9\) and \(FG = 5\). Using the segment addition postulate \(GH=FH - FG\). So \(GH=9 - 5 = 4\).

Step3: Find the length of \(EH\)

Using the segment addition postulate \(EH=EG + GH\). Substitute \(EG = 10\) and \(GH = 4\) into the formula, we get \(EH=10+4\).

Answer:

\(14\)