(i) construct the perpendicular bisector of a line segment

Step 1: Open the compasses to more than half the distance from A to B.

Step 2: Draw two arcs with centre A.

Step 3: Draw two arcs with centre B.

Step 4: Use a straight edge to complete the construction.

(ii) construct the bisector of an angle

Step 1: Using compasses, draw an arc with centre O, so it cuts one of the original lines. Call this point A.

Step 2: Without changing the compass setting, construct a second arc with centre O, to cut the other line at B.

Step 3: Construct two further arcs with centres A and B.

Step 4: Complete the construction by drawing a straight line from O to the point of intersection.