Constructions use only a compass and straight edge (no measuring). The three standard constructions you must know are:
1. Perpendicular bisector of a line segment AB: Open the compass to more than half the length of AB. Draw arcs above and below the line from both A and B. Connect the two intersections — this line is the perpendicular bisector and the locus of points equidistant from A and B.
2. Angle bisector: Place the compass at the vertex and draw an arc crossing both arms. From each crossing point, draw equal arcs inside the angle. Connect the vertex to where the arcs meet — this bisects the angle exactly.
3. Perpendicular from a point to a line: Place the compass at the point and draw two arcs that cross the line. From those two crossings, draw equal arcs on the other side. Connect the original point to the new intersection.
Always leave your construction arcs visible — erasing them loses the marks.
Common error: measuring with a ruler to check accuracy instead of relying on the compass construction — the examiner wants to see the arcs, not a measured result.