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.

Start practising Read the lesson

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) Using ruler and compasses, construct triangle $ABC$ with $AB = 7$ cm, $BC = 6$ cm and $AC = 5$ cm.

(b) Construct the perpendicular bisector of $BC$ and the bisector of angle $BAC$ . Extend both constructed lines far enough for them to cross, and mark the crossing point $X$ . (You may find that $X$ lies outside the triangle.)

(c) Ravi says " $X$ is the same distance from $B$ as from $C$ , and it is also the same distance from $AB$ as from $AC$ ." Explain why Ravi is right.
Level 5 · 6 marksTry it
2
Using ruler and compasses only, construct an angle of $75°$ . You must show all your construction arcs.

Hint: $75 = 60 + 15$ .
Level 5 · 4 marksTry it