Constructions
This interactive worksheet practises ruler-and-compass constructions.
You will construct perpendicular bisectors, angle bisectors, equilateral triangles, and specific angles. A virtual pair of compasses and a ruler are provided for you to construct your answers accurately. Jump to the questions
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Worksheet preview and key skills
Worksheet preview
This worksheet provides 7 interactive questions focusing on pure ruler-and-compass constructions.
You will use virtual tools to construct bisectors, perpendiculars, triangles, and specific angles. You must show the correct construction marks (arcs and circles) to earn the mark.
What you’ll practise
- Constructing the perpendicular bisector of a line segment.
- Bisecting a given angle.
- Constructing a perpendicular from a point to a line.
- Constructing 60°, 30°, and 45° angles.
Use the interactive worksheet below, or read the Topic guide for the method and worked example.
Constructions
Use the virtual pair of compasses and ruler to complete the constructions. You must show all construction arcs. Select a tool to begin.
Topic guide
Constructions use only a pair of compasses and a ruler (used only for drawing straight lines, not for measuring) to draw geometrically accurate figures.
Key construction: The perpendicular bisector
The perpendicular bisector cuts a line segment exactly in half at a 90° angle. It is the foundation for many other constructions.
- Place the point of your compasses on one end of the line segment.
- Open the compasses so the radius is clearly greater than half the length of the line.
- Draw a circle (or large arcs above and below the line).
- Keep the compasses at the exact same width and place the point on the other end of the line.
- Draw another circle.
- Use your straightedge to draw a line passing directly through the two points where the circles intersect.
Constructing a 60° angle
- Start with a straight line and mark a point on it to be the vertex of your angle.
- Place the compass point on the vertex and draw a circle that crosses the line. Keep the compass width exactly the same!
- Move the compass point to the intersection where the circle crossed the line.
- Draw a second circle.
- Draw a straight line from the original vertex through the point where the two circles intersect. This creates an exact 60° angle.
Tips for success
- Never rub out your construction arcs! They are your working out. Examiners need to see them to give you full marks.
- Make sure your pencil is sharp and your compass hinge is tight. If the width slips while drawing, your construction will be incorrect.
- To construct a 30° angle, first construct a 60° angle and then bisect it.