GCSE · Constructions & loci

Ruler-and-compass constructionsExam-style questions

The four standard constructions — perpendicular bisector, angle bisector, perpendicular from/at a point, and 60° — why each one works, and why the construction arcs must be left on the page.

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10 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
(a) Draw a straight line and mark a point $X$ on it.

Using ruler and compasses only, construct an angle of $60°$ at $X$ . You must show all your construction arcs.

(b) Hence construct an angle of $30°$ .

(c) Explain why the construction in part (a) gives exactly $60°$ .
Level 4 · 5 marksTry it
2
Elin bisects the angle at $Q$ using the standard construction: an arc centred at $Q$ cuts the two arms at points $S$ and $T$ , then equal arcs centred at $S$ and at $T$ cross at the point $U$ , and she draws the line $QU$ .

Explain why this construction bisects the angle. You should refer to the triangles $QSU$ and $QTU$ .
Level 4 · 3 marksTry it