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

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

Answer 1

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

1. Point \( E \) is the midpoint of segment \( BD \). Therefore, \( BE = DE \).
2. Since \( AC \) is the perpendicular bisector, segments \( AE \) and \( CE \) will be of equal length.

Given this information, let's analyze the options provided:

- **It must be the same length as segment \( AB \).** (Not necessarily true; this is not a given.)
- **It must be the same length as segment \( A B \).** (Same as above; can't conclude it.)
- **It must be the same length as segment \( DE \).** (True, since \( BE = DE \).)
- **It must be the same length as segment \( D E \).** (This is restating the previous option; also true.)
- **It must be the same length as segment \( BC \).** (Not necessarily true; could vary.)
- **It must be the same length as segment \( B C \).** (Same as above; can't conclude it.)
- **It must be the same length as segment \( EA \).** (Not true; \( EA \) is not necessarily equal to \( BE \).)
- **It must be the same length as segment \( C D \).** (Not true; can vary.)

Since both \( BE \) and \( DE \) are equal for the perpendicular bisector, the correct response is:

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