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Question Line segment AC¯¯¯¯¯¯¯¯ is a perpendicular bisector of segment BD¯¯¯¯¯¯¯¯ , with the two segments meeting at point E . What is true of segment BE¯¯¯¯¯¯¯¯ ? (1 point) Responses It must be the same length as segment BC¯¯¯¯¯¯¯¯ . It must be the same length as segment upper B upper C . It must be the same length as segment DE¯¯¯¯¯¯¯¯ . It must be the same length as segment upper D upper E . It must be the same length as segment EA¯¯¯¯¯¯¯¯ . It must be the same length as segment upper C upper D . It must be the same length as segment AB¯¯¯¯¯¯¯¯ .

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

  1. Perpendicular Bisector Definition: As a perpendicular bisector, AC not only bisects segment BD into two equal parts at point E but also forms right angles (90 degrees) with segment BD at that point.

  2. Segment Lengths: Since AC bisects BD at point E, we can conclude that \( BE = ED \). Because E is the midpoint of BD.

Therefore, the true statement about segment \( BE \) is:

It must be the same length as segment DE.

Thus, we can select the option: It must be the same length as segment DE.