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 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 DE¯¯¯¯¯¯¯¯.

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

1. Point \( E \) is the midpoint of segment \( BD \), meaning \( BE = ED \).
2. Since \( AC \) is perpendicular to \( BD \), all points on \( AC \) make right angles with \( BD \).

From this, we conclude that segment \( BE \) is equal to segment \( ED \).

Now, examining the provided responses, we can select which statement is true based on the properties of perpendicular bisectors:

- **It must be the same length as segment \( EA \).** (Not necessarily true, as \( A \) and \( E \) are not defined in relation to \( BD \) other than through \( AC \)).
- **It must be the same length as segment \( CD \).** (Not true as the relationship isn't established).
- **It must be the same length as segment \( AB \).** (Not established).
- **It must be the same length as segment \( AB \).** (Duplicate response).
- **It must be the same length as segment \( BC \).** (Not established).
- **It must be the same length as segment \( BC \).** (Duplicate response).
- **It must be the same length as segment \( DE \).** (True as \( BE = ED \)).

Thus, the correct answer is:

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