Question

point e is the midpoint of \\( \overline{ab} \\) and point f is the midpoint of \\( \overline{cd} \\).
which statements about the figure must be true? select three options.
\\( \square \overline{ab} \\) is bisected by \\( \overline{cd} \\).
\\( \square \overline{cd} \\) is bisected by \\( \overline{ab} \\).
\\( \square ae = \frac{1}{2}ab \\)
\\( \square ef = \frac{1}{2}ed \\)
\\( \square ce + ef = fd \\)

Explanation:

Step1: Analyze the mid - point definition

Since \(E\) is the mid - point of \(\overline{AB}\), by the mid - point formula, \(AE=\frac{1}{2}AB\).

Step2: Analyze the segment addition and mid - point of \(\overline{CD}\)

Since \(F\) is the mid - point of \(\overline{CD}\), \(CF = FD\). Also, \(CF=CE + EF\) (by segment addition postulate). So, \(CE + EF=FD\).

Step3: Check the bisection

There is no information to suggest that \(\overline{AB}\) is bisected by \(\overline{CD}\) or \(\overline{CD}\) is bisected by \(\overline{AB}\). For \(EF=\frac{1}{2}ED\), there is no basis as we only know \(F\) is the mid - point of \(CD\) (not related to \(ED\) in the given way).

Answer:

\(\boxed{AE=\frac{1}{2}AB}\), \(\boxed{CE + EF=FD}\)