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

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

1 answer

Since line segment AC is a perpendicular bisector of segment BD and they intersect at point E, the following can be inferred:

  1. Since E is the midpoint of segment BD (because AC is the bisector), this means segment BE is equal in length to segment DE.

Therefore, the correct answer is:

A. it must be the same length as segment DE.

Additionally, since AC is perpendicular to BD at E, we also know that angle AEB and angle CED are both right angles. However, that's not directly relevant to the specific choices given.