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Easy: Perpendicular bisector of a horizontal segment
To find a perpendicular bisector, draw two arcs of equal radius from each end of the segment. The radius must be more than half the segment's length so the arcs cross. The line through the two crossing points is the bisector. An angle bisector uses one arc across both sides of the angle, then two equal arcs from those points that cross on the bisector.
Construct each bisector with a compass and straightedge. Draw the construction on your sheet.
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Each arc must reach past the middle of the segment. A radius more than half the segment's length makes the arcs from the two ends cross; a smaller one leaves them apart.
The two crossing arcs are the same distance from the two sides, so the point where they meet is equally far from both rays. Any point on the bisector is equally far from both sides of the angle.
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