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The lines \(\Line{GH}\) and \(\Line{EI}\) intersect at \(F\), and the lines \(\Line{GE}\) and \(\Line{HI}\) are parallel. Given \(FG=3\) cm, \(FH=5\) cm, \(FI=7\) cm, and \(HI=9\) cm:
Calculate the lengths \(FE\) and \(EG\). Justify.
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