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? select three options.
\\( \square \overline { a b } \\) is bisected by \\( \overline { c d } \\).
\\( \square \overline { c d } \\) is bisected by \\( \overline { a b } \\).
\\( \square a e = \frac { 1 } { 2 } a b \\)
\\( \square e f = \frac { 1 } { 2 } e d \\)
\\( \square c e + e f = f d \\)

Explanation:

Step1: Analyze the mid - point property

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

Step2: Analyze the segment addition property

Since \(F\) is the mid - point of \(\overline{CD}\), we know that \(CF = FD\). Also, \(CF=CE + EF\) (by the segment addition postulate: if \(C\), \(E\), \(F\) are collinear, then \(CF=CE + EF\)). So \(CE + EF=FD\).

Answer:

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