Using a compass and ruler to bisect, construct and build angles and shapes.
Practise Construction of geometric figures in the app →
What gets asked
- Bisect a line segment or an angle using a compass.
- Construct a perpendicular line at or from a point.
- Construct a triangle or quadrilateral from given measurements.
- Construct a 30°, 45° or 60° angle without a protractor.
You must be able to
- Keep the compass width the same while drawing a pair of arcs.
- Use a compass to bisect a line or an angle exactly.
- Transfer each given length accurately with a compass, not by eye.
- Build up an angle such as 120° from 60° angles using a compass.
Traps that cost marks
- Changing the compass width partway through a bisection, so the arcs do not cross where they should. Set the compass once and keep that width for both arcs of a bisection.
- Measuring an angle with a protractor instead of constructing it with a compass. A construction question needs compass and ruler marks, not a protractor reading.
- Drawing a triangle to look roughly right instead of transferring each length with the compass. Set your compass to the exact length given, and use it to mark that length on the page.
- Using a protractor to draw a right angle instead of constructing the perpendicular. A perpendicular construction uses arcs from the given point, not a protractor reading of 90°.
Worked example
Bisect a given angle using only a compass and a ruler.
- Put the compass point on the vertex and draw an arc crossing both arms of the angle.
- From each of those two crossing points, draw two more equal arcs that cross each other inside the angle.
- Join the vertex to the point where those two arcs cross. That line bisects the angle.