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
The diagram shows an angle $PQR$ .Using ruler and compasses only, construct the bisector of angle $PQR$ . You must show all your construction arcs.
Level 3 · 3 marksTry it
2
The diagram shows a straight line $l$ , a point $P$ which is not on the line, and a point $Q$ which is on the line.(a) Using ruler and compasses only, construct the perpendicular from $P$ to the line $l$ . You must show all your construction arcs.

(b) Using ruler and compasses only, construct the perpendicular to $l$ at the point $Q$ .

(c) Aisha says "the perpendicular I drew in part (a) is the shortest path from $P$ to the line". Explain why Aisha is right.
Level 3 · 6 marksTry it
3
(a) Draw a straight line and mark a point $P$ on it. Using ruler and compasses only, construct an angle of $90°$ at $P$ .

(b) By adding one further construction, obtain an angle of $45°$ at $P$ . Show all your construction arcs.
Level 3 · 4 marksTry it
4
(a) Draw a line segment $MN$ of length $7.6$ cm. Using ruler and compasses only, construct the perpendicular bisector of $MN$ .

(b) Your bisector crosses $MN$ at the point $X$ . Write down the length of $MX$ .
Level 3 · 3 marksTry it