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.
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
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°.