4.9

Constructions and loci

Cambridge IGCSE Mathematics (0580)  · Unit 4: Geometry  · 9 flashcards

Constructions and loci is topic 4.9 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 4 — Geometry , alongside Angles, Angles in polygons and Parallel lines.  In one line: Construction refers to the precise drawing of shapes, angles, or lines using only a compass and straightedge (ruler without measurements). It relies on geometric principles to create accurate diagrams.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 9 flashcards — 2 definitions, 4 key concepts and 3 application cards — covering the precise wording mark schemes reward.  Use the 2 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

'construction' in geometry

Construction refers to the precise drawing of shapes, angles, or lines using only a compass and straightedge (ruler without measurements). It relies on geometric principles to create accurate diagrams.

Questions this Constructions and loci deck will help you answer

Definition Flip

Define 'construction' in geometry.

Answer Flip

Construction refers to the precise drawing of shapes, angles, or lines using only a compass and straightedge (ruler without measurements). It relies on geometric principles to create accurate diagrams.

Key Concept Flip

Describe how to construct the perpendicular bisector of a line segment AB.

Answer Flip

With the compass centered at A, draw arcs above and below AB. Repeat with the compass centered at B, ensuring the arcs intersect. Draw a straight line through the intersection points; this is the perpendicular bisector.

Definition Flip

Explain the meaning of 'locus'.

Answer Flip

A locus is a set of points that satisfy a specific condition. It is the path traced by a point that moves according to a given rule or set of rules.

Key Concept Flip

How do you construct the angle bisector of an angle ABC?

Answer Flip

Place the compass at vertex B and draw an arc intersecting BA and BC. From these intersection points, draw two arcs that intersect. Draw a line from B to the intersection point of the arcs. This line bisects the angle ABC.

Key Concept Flip

Describe the locus of points equidistant from a fixed point.

Answer Flip

The locus of points equidistant from a fixed point is a circle. The fixed point is the center of the circle, and the distance represents the radius.

Key Concept Flip

Describe the locus of points equidistant from two given points A and B.

Answer Flip

The locus of points equidistant from two points A and B is the perpendicular bisector of the line segment AB. Every point on the perpendicular bisector is the same distance from A and B.

Key Concept Flip

Describe the locus of points equidistant from two intersecting lines.

Answer Flip

The locus of points equidistant from two intersecting lines is a pair of angle bisectors of the angles formed by the intersecting lines. Any point on these bisectors is equidistant from both lines.

Key Concept Flip

Explain the difference between using a protractor and construction methods to draw angles.

Answer Flip

A protractor measures angles directly. Construction uses a compass and ruler to create angles based on geometric principles for accuracy.

Key Concept Flip

Outline the steps to construct a 60° angle.

Answer Flip

Draw a straight line. With the compass centered at one endpoint, draw an arc. Keeping the same compass width, place the compass at the intersection of the arc and the line, and draw another arc intersecting the first. Draw a line from the endpoint to this intersection.

Test yourself

Practice with MCQ questions to check your understanding.

Take Mathematics Quiz
4.8 Similarity and congruence 4.10 Pythagoras theorem

Key Questions: Constructions and loci

Define 'construction' in geometry.

Construction refers to the precise drawing of shapes, angles, or lines using only a compass and straightedge (ruler without measurements). It relies on geometric principles to create accurate diagrams.

Explain the meaning of 'locus'.

A locus is a set of points that satisfy a specific condition. It is the path traced by a point that moves according to a given rule or set of rules.

More topics in Unit 4 — Geometry

Constructions and loci sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

construct construction compass ruler protractor bisector perpendicular bisector angle bisector locus loci equidistant

Key terms covered in this Constructions and loci deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

'construction' in geometry
Explain the meaning of 'locus'

Related Mathematics guides

Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.

How to study this Constructions and loci deck

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