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

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

1 answer

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

  1. Point E is the midpoint of segment BD.
  2. Segment AC intersects segment BD at a right angle.

Since E is the midpoint of BD, we know that the lengths of segments BE and DE are equal. Therefore, the correct statement is:

It must be the same length as segment DE.