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 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 .
It must be the same length as segment DE¯¯¯¯¯¯¯¯.
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 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 .
It must be the same length as segment DE¯¯¯¯¯¯¯¯.
Answers
GPT-4o mini
To understand the properties of the segments based on the given information, we need to analyze what we know about the perpendicular bisector and the segments involved.
Since line segment \( AC \) is the perpendicular bisector of segment \( BD \), the following properties hold true:
1. Point \( E \) is the midpoint of segment \( BD \), which means that \( BE = ED \).
2. The perpendicular bisector implies that segment \( AC \) is perpendicular to \( BD \) at point \( E \).
From point 1, we can directly conclude that:
- \( BE = ED \)
Given the options, the most relevant conclusion is about the relationship between segments.
Since \( BE \) is equal to \( ED \) and in a perpendicular bisector scenario, \( AC \) will have congruent segments; the relationship would primarily focus on \( BE \) and others.
However, none of the options explicitly mention that \( BE = ED \). It sounds like some of the options contain segments labeled A, B, C, and D which might be misinterpreted from the original description.
With all things considered in the context of a perpendicular bisector, the most accurate statement would be regarding segment \( DE \).
In summary of the properties of segment \( BE \):
***It must be the same length as segment \( ED \).***
But since that is not listed among the provided responses and recognizing its previous form, if given closer options, one could safe conclude with an emphasis on equal segments in bisecting statements involving the bisector interaction between \( BE \) and \( DE \).
- **To summarize:** \( BE = DE \).
Since line segment \( AC \) is the perpendicular bisector of segment \( BD \), the following properties hold true:
1. Point \( E \) is the midpoint of segment \( BD \), which means that \( BE = ED \).
2. The perpendicular bisector implies that segment \( AC \) is perpendicular to \( BD \) at point \( E \).
From point 1, we can directly conclude that:
- \( BE = ED \)
Given the options, the most relevant conclusion is about the relationship between segments.
Since \( BE \) is equal to \( ED \) and in a perpendicular bisector scenario, \( AC \) will have congruent segments; the relationship would primarily focus on \( BE \) and others.
However, none of the options explicitly mention that \( BE = ED \). It sounds like some of the options contain segments labeled A, B, C, and D which might be misinterpreted from the original description.
With all things considered in the context of a perpendicular bisector, the most accurate statement would be regarding segment \( DE \).
In summary of the properties of segment \( BE \):
***It must be the same length as segment \( ED \).***
But since that is not listed among the provided responses and recognizing its previous form, if given closer options, one could safe conclude with an emphasis on equal segments in bisecting statements involving the bisector interaction between \( BE \) and \( DE \).
- **To summarize:** \( BE = DE \).