Bisecting a line segment
Draw AB = 7 cm and construct its perpendicular bisector.
Draw AB = 8 cm and construct its perpendicular bisector.
Draw AB = 9 cm and construct its perpendicular bisector.
Draw AB = 5 cm and construct its perpendicular bisector.
Draw AB = 6.4 cm and construct its perpendicular bisector.
1. Draw AB = 7 cm.
2. With A as the center and a radius more than half of AB, draw arcs above and below AB.
3. With B as the center and the same radius, draw arcs that cut the first two at P and Q.
4. Join PQ. It cuts AB at M, its midpoint: AM = MB = 3.5 cm and ∠PMB = 90°.
1. Draw AB = 8 cm.
2. With A as the center and a radius more than half of AB, draw arcs above and below AB.
3. With B as the center and the same radius, draw arcs that cut the first two at P and Q.
4. Join PQ. It cuts AB at M, its midpoint: AM = MB = 4 cm and ∠PMB = 90°.
1. Draw AB = 9 cm.
2. With A as the center and a radius more than half of AB, draw arcs above and below AB.
3. With B as the center and the same radius, draw arcs that cut the first two at P and Q.
4. Join PQ. It cuts AB at M, its midpoint: AM = MB = 4.5 cm and ∠PMB = 90°.
1. Draw AB = 5 cm.
2. With A as the center and a radius more than half of AB, draw arcs above and below AB.
3. With B as the center and the same radius, draw arcs that cut the first two at P and Q.
4. Join PQ. It cuts AB at M, its midpoint: AM = MB = 2.5 cm and ∠PMB = 90°.
1. Draw AB = 6.4 cm.
2. With A as the center and a radius more than half of AB, draw arcs above and below AB.
3. With B as the center and the same radius, draw arcs that cut the first two at P and Q.
4. Join PQ. It cuts AB at M, its midpoint: AM = MB = 3.2 cm and ∠PMB = 90°.
Why it works
P is the same distance from A as from B (the same radius), and so is Q. Every point the same distance from A and B lies on one line, the perpendicular bisector of AB, so PQ is that line.