Question

1. if (overleftrightarrow{be}) is a perpendicular bisector of (overline{ad}), which statement is true? (overline{ce}congoverline{bc}) (overline{bd}congoverline{ed}) (overline{ae}congoverline{ab}) (overline{ac}congoverline{cd})

Explanation:

Step1: Recall definition of perpendicular bisector

A perpendicular bisector of a line - segment divides the line - segment into two equal parts and is perpendicular to it. Given that $\overrightarrow{BE}$ is the perpendicular bisector of $\overline{AD}$, the point of intersection of $\overrightarrow{BE}$ and $\overline{AD}$ (point $C$) divides $\overline{AD}$ into two equal segments.

Step2: Identify equal segments

Since $C$ is the mid - point of $\overline{AD}$ due to $\overrightarrow{BE}$ being the perpendicular bisector of $\overline{AD}$, we have $\overline{AC}\cong\overline{CD}$.

Answer:

$\overline{AC}\cong\overline{CD}$