Given that line segment \( AC \) is a perpendicular bisector of segment \( BD \), this means that:
- Point \( E \) is the midpoint of segment \( BD \).
- \( BE \) is equal in length to segment \( DE \) because \( E \) divides \( BD \) into two equal parts (since it is the midpoint).
Therefore, the correct statement regarding segment \( BE \) is:
It must be the same length as segment \( DE \).
So, the answer is:
It must be the same length as segment DE.