Every line bisector divides a line into two halves: by definition!
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the bisector
A bisector cuts a line SEGMENT into two congruent line segments. A line has indefinite or infinite length.
This line is called the midpoint of the segment. It is located exactly halfway between the endpoints of the segment, dividing it into two equal segments.
CV- converse
A bisector is a line that divides another into two halves. If the second line is at right angles to the first, it is perperdicular. So, a perpendicular bisector of a side is a line which is at right angles to the side and which divides the side into two halves.