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.
'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
- › Describe how to construct the perpendicular bisector of a line segment AB.
- › How do you construct the angle bisector of an angle ABC?
- › Describe the locus of points equidistant from a fixed point.
- › Describe the locus of points equidistant from two given points A and B.
- › Describe the locus of points equidistant from two intersecting lines.
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.
Describe how to construct the perpendicular bisector of a line segment AB.
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.
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.
How do you construct the angle bisector of an angle ABC?
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.
Describe the locus of points equidistant from a fixed point.
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.
Describe the locus of points equidistant from two given points A and B.
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.
Describe the locus of points equidistant from two intersecting lines.
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.
Explain the difference between using a protractor and construction methods to draw angles.
A protractor measures angles directly. Construction uses a compass and ruler to create angles based on geometric principles for accuracy.
Outline the steps to construct a 60° angle.
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.
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.
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.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
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