Line segment AC is 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 BC
b. It must be the same length as segment DE
c. It must be the same length as segment EA
d. It must be the same length as segment AB

Answer 1

Given that line segment AC is the perpendicular bisector of segment BD, we can deduce the following about point E, where the two segments intersect:

1. Since AC is the perpendicular bisector of BD, point E is the midpoint of segment BD. This means that segments BE and DE are equal in length.

Therefore, the correct answer is:

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