Question

point e is the midpoint of \\( \overline { a b } \\) and point f is the midpoint of \\( \overline { c d } \\). which statements about the figure must be true? choose three correct answers. \\( \overline { c d } \\) is bisected by \\( \overline { a b } \\). \\( \overline { a b } \\) is bisected by \\( \overline { c d } \\). \\( c e + e f = f d \\)

Explanation:

Step1: Analyze the mid - point property

Since \(E\) is the mid - point of \(\overline{AB}\), \(AE = EB\). Since \(F\) is the mid - point of \(\overline{CD}\), \(CF=FD\). And \(CF = CE + EF\) (by the segment addition postulate).

Step2: Check each statement

• For the statement “\(\overline{CD}\) is bisected by \(\overline{AB}\)”: There is no information to suggest that \(\overline{AB}\) bisects \(\overline{CD}\). Just because \(E\) is the mid - point of \(\overline{AB}\) and \(F\) is the mid - point of \(\overline{CD}\), we cannot say \(\overline{AB}\) bisects \(\overline{CD}\).
• For the statement “\(\overline{AB}\) is bisected by \(\overline{CD}\)”: There is no information to suggest that \(\overline{CD}\) bisects \(\overline{AB}\).
• For the statement “\(CE + EF=FD\)”: By the segment addition postulate \(CF = CE + EF\), and since \(F\) is the mid - point of \(\overline{CD}\), \(CF = FD\). So \(CE + EF=FD\) is True.

Answer:

The statement \(CE + EF = FD\) is True.