Construction

• Measure and draw lines to the nearest millimetre.
• Construct triangles from three sides (compasses) or from sides and angles (protractor).
• Use a scale to turn real distances into a drawing and back.
• Construct the perpendicular bisector of a line segment with straight edge and compasses.
• Construct the bisector of an angle with straight edge and compasses.

Ruler, protractor and compasses

Measure lines to the nearest millimetre, starting from the 0 mark, not the end of the ruler. Use a sharp pencil.

Three sides known (SSS): draw one side accurately; set the compasses to the second length and draw an arc from one end; set them to the third length and draw an arc from the other end; join both ends to the point where the arcs cross.

Two sides and the included angle (SAS) or two angles and a side (ASA): draw the known side, then use a protractor to draw the angle(s) at its end(s).

Using a scale

A scale such as 1 : 50 000 means 1 cm on the drawing represents 50 000 cm in real life. Multiply to go from drawing to real; divide to go from real to drawing. Convert the units at the end: 100 cm = 1 m, 1000 m = 1 km.

Of a line segment

The perpendicular bisector cuts a line segment in half at right angles. Every point on it is the same distance from both ends.

1. Open the compasses to more than half the length of AB.
2. From A, draw arcs above and below AB.
3. Without changing the compasses, draw arcs from B to cross the first two.
4. Join the two crossing points with a straight line.

Halving an angle

The angle bisector splits an angle into two equal angles. Every point on it is the same distance from both arms.