Construction is drawing a picture or a loci using a compass and a straight edge. There are three basic constructions that you will use over and again in GCSE Mathematics: the angle bisector and the perpendicular bisector and the equalateral triangle.

To bisect a line or an angle means to cut it into exactly half. So a perpendicular bisector means to cut a line in exactly half with a line that runs at exactly 90 degrees to the line which it cuts. An angle bisector is a method used to cut an angle in exactly half.

Sometimes, you might be asked to construct a triangle with sides, say, 4cm, 7cm and 8cm in length. For this construction, instead of a straight edge, you will need a ruler so you can measure the lengths of the lines required.

Constructing a picture of a shape or an angle requires that you leave all construction lines on your drawing so that the examiner can see what you have done. If you are more than a degree or a millimetre outside the required amount, you will lose the marks so you must be accurate.

A video of how to bisect an angle. At this point, I was using a pencil in my compass and so it might be difficult to see the marks made by the pencil at times.

Cut a line exactly in half using a compass and a straight edge. Both lines will be at 90 degrees to each other. Again, this video is drawn in pencil and so it might be difficult to see at times.

This combines bisecting a line perpendicularly and then bisecting the angle of degrees formed to create an angle of 45 degrees.

A video of how to bisect an angle. This video is clearer than the first as I have a pen in the compass this time.

Circumscribing means to draw a circumference (or circle) on the outside of a shape but where the points of the shape all touch the circumference or the circle. This involves construcing the perpendicular bisectors of two of the sides and then using their interception as the centre of the circle.

Construct an angle of 60 degrees and then bisect the angle leaving you with an angle of 30 degrees.

Construct an equilateral triangle is also a way to construct an angle of 60 degrees. This is a good starting point when you want to construct an angle of 30 degrees.

This is a pdf file of notes on the construction of a perpendicular bisector and an angle bisector.

Using a ruler and a compass to draw a triangle of specified dimensions.

Inscribing means to draw a circumference (or circle) on the inside of a triangle but where each side touches the circumference or the circle. This involves construcing the angle bisectors of two of the sides and then using their interception as the centre of the circle.

Construct a line that runs at right angles to another line using a compass and a straight edge.