To consider how to bisect a line segment, start with the meaning of the word 'bisect'. To bisect is to divide into two equal pieces. When bisecting an line segment, one constructs a bisector. A bisector is something that cuts an object into two equal pieces. The bisector that will be constructed is halfway between the two end points of the line segment. The bisector is the same distance from each of the endpoints of the line segment.
Whenever you hear 'same distance', think 'circle' and 'arc'. A circle is all points that are the same distance from a center point. The bisector will be drawn using the circle tool to draw circles, and a straightedge to draw the bisector.
Manipulative 1 shows interactively how to construct the bisector of a line segment.
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