Ruler-and-compass constructions

WJEC requires constructions on Unit 1 (non-calculator) at all tiers. Marks reward construction arcs left visible — never erase them. A finished construction without arcs scores zero method marks.

Equipment

• Ruler (graduated in mm).
• Pair of compasses.
• Sharp pencil.
• Protractor not required for the construction itself, but used to verify.

Construction 1 — perpendicular bisector of a line segment AB

1. Open compasses to more than half of AB.
2. From A, draw arcs above and below AB.
3. Without changing the radius, repeat from B.
4. Join the two arc intersections — this line is the perpendicular bisector of AB.

The bisector cuts AB at right angles and at its midpoint. Every point on the bisector is equidistant from A and B. This is why locus questions use it.

Construction 2 — angle bisector of ∠BAC

1. From vertex A, draw an arc cutting AB at P and AC at Q (any radius).
2. From P and from Q (same radius), draw two arcs that intersect inside the angle at point R.
3. Draw line AR — this is the bisector.

Every point on the bisector is equidistant from the two arms.

Construction 3 — perpendicular from a point P to a line ℓ

1. From P, draw an arc cutting ℓ at two points X and Y.
2. From X and Y (same radius, larger than half XY), draw arcs intersecting on the opposite side of ℓ from P, at point Q.
3. Line PQ is perpendicular to ℓ.

Construction 4 — perpendicular at a point on a line

Similar to Construction 1 but applied to a point on the line.

Construction 5 — equilateral triangle / 60° angle

1. Draw segment AB.
2. From A, draw an arc of radius AB.
3. From B, draw an arc of the same radius.
4. The arcs intersect at C; △ABC is equilateral. ∠BAC = 60°.

WJEC exam tip

Always leave construction arcs visible. The mark scheme says explicitly "M1 for arcs of equal radii from each end". Pencil pressure should be light enough to keep them visible after.