Line segment AC¯¯¯¯¯¯¯¯

Question

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

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 .

Answer 1

Given that line segment \( AC \) is a perpendicular bisector of segment \( BD \), this means that:

1. Point \( E \) is the midpoint of segment \( BD \).
2. \( BE \) 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.