Question

look at the diagram and evaluate. which of the statements below is true? answer ( \bigcirc mathrm{df}<mathrm{fg} ) ( \bigcirc mathrm{de}=mathrm{ef} ) ( \bigcirc mathrm{dg}<mathrm{ef} ) ( \bigcirc mathrm{f} ) is the midpoint of ( overline{mathrm{eg}} )

Explanation:

Step1: Calculate the lengths

• \(DF = 15 - 5=10\)
• \(FG = 16 - 15 = 1\)
• \(DE=10 - 5 = 5\)
• \(EF=15 - 10 = 5\)
• \(DG=16 - 5=11\)
• \(EF = 5\)
• For \(F\) to be the mid - point of \(\overline{EG}\), \(EF\) should be equal to \(FG\). But \(EF = 5\) and \(FG=1\)

Step2: Analyze each option

• For \(DFFG\)
• For \(DE = EF\): Since \(DE = 5\) and \(EF = 5\), \(DE=EF\)
• For \(DGEF\)
• For \(F\) is the mid - point of \(\overline{EG}\): Since \(EF

eq FG\), \(F\) is not the mid - point of \(\overline{EG}\)

Answer:

\(DE = EF\)