Question

line segment \\( \overline { a c } \\) is a perpendicular bisector of segment \\( \overline { b d } \\), with the two segments meeting at point \\( e \\). what is true of segment \\( \overline { b e } \\)? (1 point)

\\( \bigcirc \\) it must be the same length as segment \\( \overline { e a } \\).

\\( \bigcirc \\) it must be the same length as segment \\( \overline { d e } \\).

\\( \bigcirc \\) it must be the same length as segment \\( \overline { b c } \\).

\\( \bigcirc \\) it must be the same length as segment \\( \overline { a b } \\).

Explanation:

Step1: Understand the property of perpendicular bisector

A perpendicular bisector of a segment divides the segment into two equal - length parts. 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 \(\overline{DE}\).