Topic summary · Foundation · CIE Core
Constructions summary
Constructions use ruler and compasses only: perpendicular bisectors, angle bisectors, and equilateral triangles.
Files: foundation-22 Constructions handout.pdf · foundation-22 Constructions handout answers.pdf · free public downloads · diagrams in the PDFs
Key learning points
- Perpendicular bisector: same compass width from both endpoints; join the intersections.
- Angle bisector: arc from the vertex, then equal arcs from those points.
- Leave construction arcs visible — they are part of the method mark.
Worked example 1 — Perpendicular bisector
Locus of the perpendicular bisector of ?
Working
Equidistant from A and B.
Worked example 2 — Angle bisector
Locus of an angle bisector?
Working
Equal compass arcs.
Worked example 3 — Circumcentre
Where do perpendicular bisectors of a triangle meet?
Working
Centre of circumcircle.
Worked example 4 — Why bisectors matter
What locus is the perpendicular bisector of AB?
Working
That locus idea links constructions to later geometry proofs.
Scaffolded Learning Sheet and answers (PDFs)
This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.