Loci and constructions
To draw constructions you need a pencil, ruler and a pair of compasses. Loci are used to identify areas that satisfy criteria such as a given distance from a point or halfway between two lines.
Constructing an angle
Constructing a 60° angle
To construct a 60° angle, we first draw a line of any length. Then using a compass, we use this as a base to construct an equilateral triangle.
To construct the equilateral triangle, we:
- open the compass to the same dimensions as our original line
- place the point of the compass on one end of the line and draw an arc
- repeat this at the other end and the arcs should intersect where the tip of the triangle should be
Connect the tip of the triangle to one end of the base, and you will have a 60° angle.
Constructing a 30° angle
To construct a 30° angle, you must first construct a 60° angle as above and then bisect the angle.
Constructing a 90° angle
To construct a 90° angle, you draw a base line and then construct a perpendicular bisector to leave a 90° angle.
Constructing a 45° angle
To construct a 45° angle, first construct a perpendicular bisector of a line to leave a 90° angle. Secondly, following the steps above, bisect the angle. This should leave you with a 45° angle.