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 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 .

It must be the same length as segment EA¯¯¯¯¯¯¯¯
.

Answer 1

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

1. Segment E is the midpoint of segment BD. Therefore, BE is equal to DE.
2. Since AC is perpendicular to BD at point E, the properties of the perpendicular bisector tell us that BE and DE must have equal lengths.

Thus, the correct response is:

**It must be the same length as segment DE.**