Construct the perpendicular bisector of a line segment.

Or, construct the midpoint of a line segment.

1. Begin with line segment XY.

2. Place the compass at point X. Adjust the compass radius so that it is more than (1/2)XY. Draw two arcs as shown here.

3. Without changing the compass radius, place the compass on point Y. Draw two arcs intersecting the previously drawn arcs. Label the intersection points and B.

4. Using the straightedge, draw line AB. Label the intersection point M. Point M is the midpoint of line segment XY, and line AB is perpendicular to line segment XY.

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