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)
It must be the same length as segment BC¯¯¯¯¯¯¯¯.
It must be the same length as segment EA¯¯¯¯¯¯¯¯.
It must be the same length as segment DE¯¯¯¯¯¯¯¯.
It must be the same length as segment AB¯¯¯¯¯¯¯¯.
It must be the same length as segment BC¯¯¯¯¯¯¯¯.
It must be the same length as segment EA¯¯¯¯¯¯¯¯.
It must be the same length as segment DE¯¯¯¯¯¯¯¯.
It must be the same length as segment AB¯¯¯¯¯¯¯¯.
Answers
GPT-4o mini
Since line segment \( AC \) is the perpendicular bisector of segment \( BD \), it means that it bisects segment \( BD \) into two equal halves at point \( E \). Therefore, we can conclude the following:
1. Since \( E \) is the midpoint of segment \( BD \), the lengths of segments \( BE \) and \( DE \) are equal.
2. It does not directly state any relationships between \( BE \) and \( AB \) or \( EA \), nor does it compare \( BE \) to \( BC \).
Based on that reasoning, the correct statement would be:
**It must be the same length as segment DE.**
1. Since \( E \) is the midpoint of segment \( BD \), the lengths of segments \( BE \) and \( DE \) are equal.
2. It does not directly state any relationships between \( BE \) and \( AB \) or \( EA \), nor does it compare \( BE \) to \( BC \).
Based on that reasoning, the correct statement would be:
**It must be the same length as segment DE.**