Topic summary · IGCSE handout

Constructions summary

Constructions use ruler and compasses only: perpendicular bisectors, angle bisectors, and equilateral triangles.

Open Learning Sheet — Constructions Download Constructions answers PDF

Files: 29_constructions_handout.pdf · 29_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 $AB$ ?

Working

\{P: PA=PB\}

Equidistant from A and B.

Worked example 2 — Angle bisector

Locus of an angle bisector?

Working

\text{equidistant from the arms}

Equal compass arcs.

Worked example 3 — Circumcentre

Where do perpendicular bisectors of a triangle meet?

Working

\text{circumcentre}

Centre of circumcircle.

Worked example 4 — Why bisectors matter

What locus is the perpendicular bisector of AB?

Working

\{\text{points equidistant from A and B}\}

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.

Open Learning Sheet Answers PDF

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