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
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.
Practice questions for Constructions
When constructing the perpendicular bisector of a line segment AB, what must you do with your compass?
Explain why compass arcs are used in geometric constructions rather than measuring with a ruler or protractor.
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°.