Drawing a Perpendicular Bisector

On any given segment, a compass and a straightedge can be used to draw its perpendicular bisector.

To draw the perpendicular bisector of a segment, these three steps can be followed.

Draw an Arc Centered at

A

Begin by placing the sharp end of the compass at one of the endpoints of the segment. Then, draw an arc with a radius larger than half the length of the segment.

Draw an Arc Centered at

B

with the Same Radius

Keeping the same compass length, draw another arc on the opposite side. Since the measure of the compass is greater than half the length of the segment, the two arcs should intersect at two distinct points.

Draw the Line Through the Points of Intersections of Arcs

Using a straightedge, draw the line through the points of intersection of the arcs.

This line is perpendicular to the given segment and their intersection is at the midpoint of the segment. Therefore, it is the desired perpendicular bisector.

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