The correct response is: "It must be the same length as segment DE¯¯¯¯¯¯¯¯." This is because AC is defined as the perpendicular bisector of segment BD, which means it not only bisects BD at point E but also creates right angles with it. As a consequence of this perpendicular bisector property, the segments BE and DE must be equal in length, since E is the midpoint of BD. This relationship is a fundamental characteristic of the perpendicular bisector that ensures that both segments are symmetrical about point E. Additionally, because AC bisects BD, any point on AC that is equidistant from both endpoints of BD must produce equal segments BE and DE. Thus, we can conclude that BE = DE, confirming that segment BE must indeed be the same length as segment DE.
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 which answer is correct and why by explaning in a 6 sentence paragraph
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¯¯¯¯¯¯¯¯.
It must be the same length as segment upper D upper E .
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 .
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