Line segment AC is a perpendicular bisector of segment BD, with the two segments meeting at point E. What is true of segment BE?

Question

A. It must be the same length as segment AB.
B. It must be the same length as segment BC.
C. It must be the same length as segment EA.
D. It must be the same length as segment DE.

Answer 1

Since line segment AC is a perpendicular bisector of segment BD, we have the following key properties:

1. It intersects segment BD at its midpoint, point E.
2. It forms right angles with segment BD at point E.

Because E is the midpoint of BD, it follows that segments BE and DE are equal in length. Therefore, we can conclude that:

D. It must be the same length as segment DE.

So, the correct answer is D.