Learning pack · IGCSE handout

Constructions

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Constructions use ruler and compasses only: perpendicular bisectors, angle bisectors, and equilateral triangles.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

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Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 📖 Full summary

Files: 29_constructions_handout.pdf · 29_constructions_handout_answers.pdf

Full topic summary

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

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.

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Browse the hub Learning Packs & Summary, or open the compact Constructions summary.