Constructions & Loci

Spec reference: Geometry and measures - Properties and constructions
Key idea: Construct geometric shapes and diagrams accurately using compasses and straight edge. Understand loci.

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Required constructions

Construction	Method
Perpendicular bisector of a line AB	Open compasses to over half AB. Draw arcs from A and B (same radius). Join intersection points.
Angle bisector	Open compasses. Draw arcs from the vertex on each arm. Draw arcs from where they cross. Join vertex to intersection.
Perpendicular from a point to a line	Draw arcs from the point crossing the line twice. Construct perpendicular bisector of that chord.
60° angle	Draw a line. Open compasses to the length of the line. Draw arcs from each end. Join.

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Loci

A locus (plural: loci) is the set of all points satisfying a given condition.

Condition	Locus
Fixed distance from a point	Circle
Equal distance from two points	Perpendicular bisector of the line joining them
Fixed distance from a line	Two parallel lines either side
Equal distance from two intersecting lines	Angle bisector

Exam tip

Always leave construction arcs visible - do not erase them.

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Test Yourself

Question 1 of 5

Locus equidistant from two points A and B?