Proofs About Angles Quick Check

Question

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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 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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Answer 1

Given that line segment \( AC \) is a perpendicular bisector of segment \( BD \) and they meet at point \( E \), we know the following properties hold true:

1. Perpendicular Bisector: A line segment that is a perpendicular bisector means that it divides another line segment into two equal parts at a right angle.

2. Segments \( BE \) and \( ED \): Since \( AC \) is the bisector of \( BD \), it implies that \( BE = ED \). This is because the perpendicular bisector cuts \( BD \) into two equal halves at point \( E \).

Based on the information given, the correct response regarding segment \( BE \) is:

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

The other statements do not hold true in relation to the properties of a perpendicular bisector.