Line Segment Bisector
From Latin: bi  "two" , secare "to cut,"
Definition: A line, ray or segment which cuts another line segment into two equal parts.
Try this Drag one of the orange dots at A or B and note the the line AB always
divides the line PQ into two equal parts.
In general 'to bisect' something means to cut it into two equal parts. The 'bisector' is the thing doing the cutting.
With a line bisector, we are cutting a line segment into two equal lengths with another line  the bisector.
In the figure above, the line PQ
is being cut into two equal lengths (PF and FQ) by the bisector line AB.
If AB crosses at a right angle, it is called the
"perpendicular bisector"
of PQ. If it crosses at any other angle it is simply called a bisector.
Drag the points A or B and see both types.
For obvious reasons, the point F is called the midpoint of the line PQ
See also Angle bisector.
How to bisect a line segment
Obviously, one way to bisect a line segment is to measure its length, divide that by two and mark the midpoint.
But you can do it without any measurement at all using just a compass and straightedge using techniques developed thousands of years ago by the Greeks.
For an animated demonstration of how to do this see
Perpendicular bisector of a line segment
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