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? choose three correct answers. $overline{ab}$ is bisected by $overline{cd}$. $ce + ef=fd$ $ef=\frac{1}{2}ed$ $overline{cd}$ is bisected by $overline{ab}$. $ae=\frac{1}{2}ab$

Explanation:

Step1: Recall mid - point property

By definition, if E is mid - point of $\overline{AB}$, then $AE=\frac{1}{2}AB$.

Step2: Analyze line - segment relationships

Since F is mid - point of $\overline{CD}$, $CF = FD$ and $EF+CE=CF = FD$.

Step3: Check bisection

There is no information to suggest $\overline{AB}$ is bisected by $\overline{CD}$ or vice - versa.

Answer:

CE + EF = FD, EF = $\frac{1}{2}$ED, AE = $\frac{1}{2}$AB