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

Question

It must be the same length as segment DE
It must be the same length as segment BC
It must be the same length as segment AB
It must be the same length as segment EA

Answer 1

Since line segment AC is the perpendicular bisector of segment BD, it means that:

1. Point E is the midpoint of segment BD, which implies that \( BE = DE \).
2. Segment AC is perpendicular to segment BD, meaning that angle BED is a right angle.

Based on this information, the correct statement is:

It must be the same length as segment DE.

Thus, the answer is: It must be the same length as segment DE.