WAEC 2008 · Paper 2 · Q11

(a)
Using a ruler and a pair of compasses only, construct a quadrilateral $PQRS$ in which $|QR| = 6\text{ cm}$ , $\angle PQR = 90^\circ$ , $\angle QRS = 120^\circ$ , $|RS| = 8\text{ cm}$ and $|PQ| = |PS|$ .
Model answer
Draw $QR = 6\text{ cm}$ . Construct $90^\circ$ at $Q$ and $120^\circ$ at $R$ (on the same side), and mark $S$ with $RS = 8\text{ cm}$ . Join $QS$ and construct its perpendicular bisector; $P$ is where it cuts the perpendicular at $Q$ . Join $PS$ .
(b)
Measure $|PQ|$ .

Worked solution (try it first)

Draw $QR = 6\text{ cm}$ .
At $Q$ , construct $90^\circ$ (bisect a straight angle).
At $R$ , construct $120^\circ$ ( $60^\circ$ twice) on the same side as the $90^\circ$ arm.
Mark $S$ on the $120^\circ$ arm with $RS = 8\text{ cm}$ .
$|PQ| = |PS|$ means $P$ is equidistant from $Q$ and $S$ , so $P$ lies on the perpendicular bisector of $QS$ .
Join $QS$ and construct its perpendicular bisector.
$P$ is where this bisector cuts the $90^\circ$ arm at $Q$ .
Join $PS$ to complete $PQRS$ .