What is the procedure to bisect a line segment?

To bisect a line segment, use a compass and straightedge to find and mark its midpoint.

First, draw the line segment you wish to bisect and label its endpoints as A and B. Place the compass point on endpoint A and adjust its width to more than half the length of the line segment. Draw an arc above and below the line segment. Without changing the compass width, place the compass point on endpoint B and draw another set of arcs that intersect the first set of arcs.

Next, use a straightedge to draw a line through the points where the arcs intersect. This line will cross the original line segment at its midpoint, effectively bisecting it. Label the midpoint as M. Now, AM and MB are equal in length, meaning the line segment AB has been successfully bisected.

This method ensures precision and is a fundamental skill in geometry, useful for various constructions and proofs.