Question

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 EA¯¯¯¯¯¯¯¯.
It must be the same length as segment upper C upper D .

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 AB¯¯¯¯¯¯¯¯.
It must be the same length as segment upper A upper B .

It must be the same length as segment BC¯¯¯¯¯¯¯¯.
It must be the same length as segment upper B upper C .
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Answer 1

Given that line segment \( AC \) is a perpendicular bisector of segment \( BD \) and that they intersect at point \( E \), we can establish several properties based on the definition of a perpendicular bisector.

1. Since \( AC \) is the **perpendicular bisector** of \( BD \):
- \( E \) is the midpoint of \( BD \).
- This means that \( BE \) is equal in length to \( DE \).

Given this information, we can conclude:

- \( BE = DE \) (since \( E \) is the midpoint of \( BD \))

This leads us to the correct response to the question regarding segment \( BE \):

**It must be the same length as segment \( DE \).**