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Knowledge Organiser: Constructions
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
Now try it yourself
Quiz · Question 1 of 10
When constructing the perpendicular bisector of a line segment AB, what must you do with your compass?
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