Question

4.3 perpendicular bisector theorem
mallory cameron
open - ended question
we know from the problem that bf = df, so what does the perpendicular bisector theorem tell us?
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Explanation:

Step1: Recall perpendicular - bisector theorem

The perpendicular - bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Step2: Analyze given condition

We are given that \(BF = DF\). According to the converse of the perpendicular - bisector theorem, if two points are equidistant from the endpoints of a segment, then the line joining them is the perpendicular bisector of the segment. So, point \(F\) lies on the perpendicular bisector of segment \(BD\).

Answer:

Point \(F\) lies on the perpendicular bisector of segment \(BD\) because if \(BF = DF\), by the converse of the perpendicular - bisector theorem, a point that is equidistant from the endpoints of a segment lies on the perpendicular bisector of that segment.