Question

overleftrightarrow{cd} is the perpendicular bisector of overline{ab}. g is the midpoint of overline{ab}. points e and f lie on overleftarrow{cl} which pair of line segments must be congruent?
○ a. overline{af} and overline{be}
○ b. overline{bf} and overline{be}
○ c. overline{ag} and overline{be}
○ d. overline{ae} and overline{be}

Explanation:

Step1: Recall the perpendicular bisector theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Since \(CD\) is the perpendicular bisector of \(AB\) and \(E\) lies on \(CD\), by the perpendicular bisector theorem, \(AE = BE\).

Answer:

D. \(\overline{AE}\) and \(\overline{BE}\)