Question
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 BC¯¯¯¯¯¯¯¯ . It must be the same length as segment upper B upper C . 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 . It must be the same length as segment AB¯¯¯¯¯¯¯¯ .
Answers
GPT-4o mini
Since segment AC is the perpendicular bisector of segment BD and they meet at point E, the following properties can be inferred:
1. **Perpendicular Bisector Definition**: As a perpendicular bisector, AC not only bisects segment BD into two equal parts at point E but also forms right angles (90 degrees) with segment BD at that point.
2. **Segment Lengths**: Since AC bisects BD at point E, we can conclude that \( BE = ED \). Because E is the midpoint of BD.
Therefore, the true statement about segment \( BE \) is:
**It must be the same length as segment DE.**
Thus, we can select the option: **It must be the same length as segment DE.**
1. **Perpendicular Bisector Definition**: As a perpendicular bisector, AC not only bisects segment BD into two equal parts at point E but also forms right angles (90 degrees) with segment BD at that point.
2. **Segment Lengths**: Since AC bisects BD at point E, we can conclude that \( BE = ED \). Because E is the midpoint of BD.
Therefore, the true statement about segment \( BE \) is:
**It must be the same length as segment DE.**
Thus, we can select the option: **It must be the same length as segment DE.**