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Can a segment have more than one perpendicular bisector?
No. All segments have only one perpendicular bisector.
How do you find a segment bisector?
Adjust a compass so the distance between the point and the pencil is more than half of the length of the segment. With the point at one end of the segment draw an arc that intersects the segment. Without adjusting the compass, with the point at the other end of the segment draw an arc that intersects the first arc at two places. The line that includes those two intersecting points is the perpendicular bisector.
How do you get a perpendicular bisector on a line segment?
Set a compass to draw a circle with a radius that's more than half the length of the line segment but less than the whole length.Put the compass point at one end of the segment and draw an arc above the middle of the segment and another below the middle of the segment.Put the compass point at the other end of the segment and again draw arcs above and below the middle of the segment, intersecting the first two arcs.Draw a line connecting the point where the two arcs intersect above the segment and the point where they intersect below the segment.That's your perpendicular bisector.
How do you find a point which is equidistant from two other points?
-- Draw a line segment from one point to the other.-- Construct the perpendicular bisector of the line segment..-- Every point on the perpendicular bisector of the line segmentis equidistant from the two original points.==========================================================================Whereupon the first contributor observed:Yes, that works, no matter how you set the compass, as long as it's more than 1/2 the distancebetween the two points. Every setting of the compass will give you a pair of points that areequal distances from the original two. As you find more and more of them ... with differentsettings of the compass ... you'll see that all the equal-distance points you're finding all lieon the same straight line. That line is the perpendicular bisector of the line between the twooriginal points, just as we described up above.
Is it possible to construct a perpendicular bisector to any given line segment using only a straightedge and a compas?
Yes Set the compass to wider than half the length of the line segment. Put the point of the compass on one end of the line segment and draw two arcs, one either side of the line (roughly near the middle). Put the point of the compass on the other end of the line segment and draw two further arcs to intersect the first two arcs. With a straight edge, join the two points where the arcs cross. This line is the perpendicular bisector of the original line segment.
