How do I construct a perpendicular bisector of a line segment using a compass?

Steps: 1) Draw line segment AB = 8cm. 2) Open compass to MORE than 4cm (more than half AB — your teacher is correct). 3) Place compass at A, draw arcs above and below the line. 4) Without changing compass width, place at B, draw arcs above and below the line (crossing the first arcs). 5) Label intersection points of arcs as P and Q. 6) Join PQ. PQ is the perpendicular bisector of AB, meeting AB at its midpoint M. Why compass must be > half: if you open to exactly half, the arcs only just touch at the midpoint and you cannot draw a line. If you open to less than half, the arcs do not intersect at all. Opening to more than half ensures clear intersection points above and below the line.