Question

line segment ( overline{ac} ) is a perpendicular bisector of segment ( overline{bd} ), with the two segments meeting at point ( e ). what is true of segment ( overline{be} )? (1 point)

it must be the same length as segment ( overline{ea} ).

it must be the same length as segment ( overline{bc} ).

it must be the same length as segment ( overline{de} ).

it must be the same length as segment ( overline{ab} )

Explanation:

Step1: Recall the definition of a perpendicular bisector

A perpendicular bisector of a segment divides the segment into two equal - length parts.

Step2: Apply the definition to the given problem

Since \(\overline{AC}\) is the perpendicular bisector of \(\overline{BD}\) and they meet at point \(E\), by the definition of a perpendicular bisector, \(BE = DE\).

Answer:

It must be the same length as segment \(\overline{DE}\)