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Geometry & MeasuresTopic Summary

Knowledge Organiser: Constructions

Part of Constructions · GCSE GCSE Mathematics revision

This topic summary covers Knowledge Organiser: Constructions within Constructions for GCSE Mathematics. Revise Constructions in Geometry & Measures for GCSE Mathematics with 10 exam-style questions and 5 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 1 of 1 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 1

Practice

10 questions

Recall

5 flashcards

Knowledge Organiser: Constructions

Key Terms
  • Construction: An accurate drawing made using only a ruler and compasses (no protractor)
  • Perpendicular bisector: A line at 90° that cuts another line exactly in half
  • Angle bisector: A line that cuts an angle exactly in half
  • Arc: Part of a circle drawn with compasses
  • Equilateral triangle: All sides equal — constructed with two arcs of the same radius
Must-Know Constructions
  • Perpendicular bisector of a line: arcs from each end (same radius > half the line) — join intersections
  • Angle bisector: arcs from vertex then from intersection points — join to vertex
  • Perpendicular from a point to a line: arcs from the point cutting the line, then bisect
  • Equilateral triangle: set compass to side length, arc from each end
  • Leave all construction arcs visible — rubbing out loses marks
Key Methods
  • Always use sharp pencil and compasses for accuracy
  • Perpendicular bisector: open compass > ½ length; arc from A, arc from B; join crossings
  • Angle bisector: arc from vertex touches both arms; arcs from each arm intersection; join to vertex
  • Never change compass width mid-construction
Key Formulas
  • Perpendicular bisector: bisects the line at 90°
  • Angle bisector: divides an angle into two equal halves
  • 60° angle: construct equilateral triangle (all sides equal to the base)
  • Perpendicular from a point to a line: arc intersects line twice, then bisect the chord
Common Mistakes
  • Erasing construction arcs: Always leave all arcs visible — the examiner needs to see your method
  • Compass width too small: For perpendicular bisector, compass must be set to MORE than half the line length
  • Changing compass width mid-construction: For bisectors, the compass width must stay the same for both arcs
  • Using a ruler to measure: Standard constructions must use compasses and ruler only — no protractor unless specifically asked

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Practice Questions for Constructions

When constructing the perpendicular bisector of a line segment AB, what must you do with your compass?

  • A. Set the compass to exactly half the length of AB, then draw arcs from A and B
  • B. Set the compass to more than half the length of AB, then draw arcs from A and B that intersect above and below the line
  • C. Set the compass to the full length of AB and draw a single arc from A
  • D. Set the compass to any radius and draw a single arc from the midpoint of AB
1 markfoundation

Explain why compass arcs are used in geometric constructions rather than measuring with a ruler or protractor.

2 markshigher

Quick Recall Flashcards

Angle Bisector
Line dividing angle into two equal parts. Locus of points equidistant from two lines. Compass arcs from vertex crossing both arms.
60° Construction
Draw arc from point, then arc of same radius from first intersection. Creates equilateral triangle principle. All angles 60°.

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Constructions

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Constructions