Which two tools are required to perform an accurate geometrical construction?
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Practise IGCSE 0580 questions in the style of recent Extended past papers, organised by syllabus subtopic. Each set comes with an examiner-style mark scheme and a downloadable worksheet.
Everything students ask about Cambridge IGCSE 0580 Geometrical constructions Topical Past Papers.
Top questions students ask on this sub-topic
These Geometrical constructions Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Geometry (E4.2) section of the 2025–2027 syllabus. Use them to revise the exact skills examiners test in this part of the course.
Each question is graded Easy → Medium → Hard, plus an A★ Challenge for top-grade preparation. Tap a question to mark your own answer, then unlock the examiner-style mark scheme with model solutions and examiner tips. A printable Topical Past Papers worksheet is included so you can practise offline.
Measure and draw lines and angles; construct triangles given lengths or angles; use ruler-and-compass constructions for bisectors and perpendiculars.
Which two tools are required to perform an accurate geometrical construction?
Describe what is meant by the perpendicular bisector of a line segment AB.
[1 mark]Describe the first step in constructing the bisector of an angle ABC using only a pair of compasses and a straight edge.
[2 marks]Two students each construct a triangle with sides of length 5 cm, 7 cm and 9 cm. Will their triangles be congruent? Justify your answer.
[2 marks]Which of the following sets of side lengths CANNOT form a triangle?
A treasure is buried at a point P that is equidistant from two trees A and B.
Describe the locus of all points equidistant from A and B.
[1 mark]The treasure is also exactly 10 m from tree A. State the maximum number of possible burial points.
[2 marks]A path is to be made equidistant from two straight fences that meet at a point at an angle of 70°. Describe the shape of the path.
[2 marks]A point P is equidistant from two points A and B, and is also exactly 5 cm from A. Describe the two ruler-and-compass constructions needed to find all possible positions of P.
[2 marks]