Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Geometric Constructions — bisectors, perpendiculars, standard triangles and loci — to become a reliable source of marks instead of rough sketches that lose accuracy marks.
What query it owns: how to understand and revise Geometric Constructions in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Geometric Constructions revision-guide angle, while Tutopiya’s Geometric Constructions subtopic page owns the learning resource and the free Geometric Constructions quiz owns the practice.

Geometric Constructions are tested on Cambridge IGCSE Mathematics (0580/0607) Paper 2 and Paper 4 with compasses and ruler — or, increasingly, with clear construction arcs shown on printed diagrams. Examiners award marks for correct method and visible arcs, not just the final line. This guide explains exactly what Geometric Constructions covers, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• Construction questions require compasses and a straight edge — freehand drawing loses method marks.
• Perpendicular bisector of a line: equidistant from both endpoints; passes through the midpoint.
• Angle bisector divides an angle into two equal parts — used in loci and triangle construction.
• Loci are paths of points satisfying a rule — often built from bisectors and arcs.

What are Geometric Constructions in Cambridge IGCSE Maths?

Geometric Constructions are accurate drawings made with compasses and a ruler, without measuring angles or lengths with a protractor or scale (except where the question allows). In Cambridge IGCSE Mathematics you construct perpendicular bisectors, angle bisectors, perpendiculars from a point, standard triangles (60°, 90°), and loci such as points equidistant from two lines or a fixed distance from a point.

You can read the full explanation, worked examples and notes on Tutopiya’s Geometric Constructions subtopic page before you attempt questions.

The core constructions you must master

These five constructions appear most often. Learn the steps and what construction arcs examiners expect to see.

Construction	What it produces	Typical exam use
Perpendicular bisector	Line at 90° through midpoint	Locus equidistant from A and B
Angle bisector	Line splitting an angle in half	Locus equidistant from two lines
Perpendicular from a point	90° line from point to line	Height of triangle
60° angle	Equilateral triangle method	Constructing standard angles
Locus (distance from point)	Arc or full circle	”Points within 3 cm of P”

How to construct a perpendicular bisector — step by step

This method is the template for many loci questions.

1. Open compasses to more than half the length of the line AB.
2. Draw arcs above and below AB from A, then repeat from B — same compass width.
3. Join the two intersection points of the arcs with a straight line.
4. The line is the perpendicular bisector — it crosses AB at its midpoint at 90°.
5. Leave all arcs visible — examiners check construction lines.
6. Label the final line and any required points.

Once you have worked through a few, test yourself with the free Geometric Constructions quiz — it tells you fast whether the methods have actually stuck.

Construction vs locus: which does the question want?

Students lose marks by drawing a line without showing arcs, or by confusing bisector types. Use the wording to decide.

Question type	Construction needed	Signal words
Equidistant from two points	Perpendicular bisector	”same distance from A and B”
Equidistant from two lines	Angle bisector	”same distance from lines PQ and RS”
Fixed distance from a point	Arc or circle	”within 4 cm of O”, “locus of points…”
Triangle given sides/angles	Intersection of arcs or bisectors	”Construct triangle ABC such that…”

Geometric Constructions in past-paper wording: command words that matter

Most lost marks come from missing arcs or using a protractor when compasses are required.

Command word / phrase	What the question wants	Typical Constructions stem
Construct	Accurate drawing with arcs shown	”Construct the perpendicular bisector of AB.”
Draw the locus	Shade or draw path of points	”Draw the locus of points 3 cm from P.”
Using compasses and a straight edge	No protractor for angles	”Using compasses and a straight edge only, construct…”
Show all construction lines	Arcs must remain visible	”Show all your construction arcs clearly.”
Mark and label	Name key points on the locus	”Mark the region that satisfies…”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the drawing — is what method marks reward. Here is how three real-style stems are answered.

1. “Construct the perpendicular bisector of line PQ.” Arcs from P and Q (radius > ½PQ), join arc intersections. Mark-scheme reward: correct arcs from both ends, perpendicular line through midpoint.
2. “Construct the locus of points equidistant from lines AB and AC.” This is the angle bisector at A. Arc method across the angle, then join A to the arc intersection. Reward: angle bisector with visible arcs.
3. “Construct triangle ABC with AB = 7 cm, BC = 5 cm and angle ABC = 60°.” Draw AB = 7 cm, construct 60° at B, mark BC = 5 cm on the ray, join C to A. Reward: correct 60° construction and side lengths.

When you can recognise the wording instantly, work the full set on the Geometry topical past-paper questions and the Geometric Constructions quiz to lock the method in.

How Geometric Constructions connect to the rest of Geometry

Constructions underpin loci questions and support triangle proofs in Similarity and Circle Theorems. Perpendicular bisectors link to chord properties of circles. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Rubbing out construction arcs — examiners cannot award method marks without them.
• Using a protractor when the question specifies compasses and straight edge only.
• Setting compass width too small for perpendicular bisector arcs (arcs do not cross).
• Confusing perpendicular bisector (two points) with angle bisector (two lines).
• Drawing a full circle when the question asks for an arc only within a region.

When you need more support

If Construction questions keep tripping you up — especially combined loci problems — work through the Geometry topical past-paper questions and the Geometric Constructions quiz to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Are Geometric Constructions hard in Cambridge IGCSE Maths? The steps are fixed and learnable. Marks are lost when students skip arcs or use the wrong bisector for a locus question.

What equipment do I need for construction questions? A pair of compasses, a ruler (straight edge) and a sharp pencil. A protractor is only used when the question allows it.

What is the difference between a perpendicular bisector and an angle bisector? A perpendicular bisector cuts a line segment in half at 90°. An angle bisector splits an angle into two equal parts.

How do I revise Geometric Constructions effectively? Practise each construction on blank paper, leave arcs visible, then take the Geometric Constructions quiz. Redo any loci question where you drew the wrong bisector.

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