Constructions
Get to grips with constructions using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on accurate ruler-and-compass constructions, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Keep the compass radius fixed and leave your construction arcs visible.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
Constructions are accurate drawings made with only a ruler and a pair of compasses. Measuring angles with a protractor is not allowed, and the construction arcs must be left visible.
Those arcs are the evidence of your method, and marks are awarded for them. Rubbing them out loses marks even when the final drawing is perfect.
Three constructions are required: the perpendicular bisector of a line, the bisector of an angle, and a perpendicular from or to a point on a line. Each uses the same basic idea — that points equidistant from two others lie on a specific line.
Revision notes
Perpendicular bisector
Open the compasses to more than half the line's length. From each end, draw arcs above and below the line, then join where they cross.
The resulting line is perpendicular to the original and passes through its midpoint. Every point on it is equidistant from the two ends.
Angle bisector
Place the compass point on the vertex and draw an arc crossing both arms. From each crossing point, draw arcs that meet, then join that meeting point to the vertex.
The line divides the angle into two equal halves, and every point on it is equidistant from the two arms.
Perpendicular from a point
From the point, draw an arc crossing the line twice. From each crossing, draw arcs that meet, then join that point to the original point.
The same compass technique appears in all three constructions, which is why practising one helps with the others.
Key points
- Use only a ruler and compasses.
- Leave all construction arcs visible.
- A perpendicular bisector cuts a line in half at right angles.
- An angle bisector divides an angle into two equal parts.
- Points on a perpendicular bisector are equidistant from the ends.
- Points on an angle bisector are equidistant from the arms.
Worked examples
Example 1
Which construction gives points equidistant from two fixed points?
Working
Example 2
Which construction gives points equidistant from two lines?
Working
Example 3
Why must construction arcs be left on the diagram?
Working
Common mistakes
Rubbing out the construction arcs.
They are the evidence of your method and carry marks.
Using a protractor.
Constructions must use only a ruler and compasses.
Changing the compass setting mid-construction.
Keep the same radius where the method requires it.
Opening the compasses to less than half the line.
The arcs will not cross, so the perpendicular bisector cannot be drawn.
Exam tips
- Keep your pencil sharp and the compasses tight.
- Never erase the arcs.
- Open the compasses to more than half the line for a bisector.
- Practise all three constructions until they are automatic.
Key terms
- Construction
- An accurate drawing using ruler and compasses only.
- Perpendicular bisector
- A line cutting another in half at right angles.
- Angle bisector
- A line dividing an angle into two equal parts.
- Equidistant
- The same distance from two things.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.