Using a ruler and a pair of compasses only…

Question 1 Report

Using a ruler and a pair of compasses only, construct (a) triangle QRT with |QR| = 8cm, |RT| = 6cm and |QT| = 4.5cm.

(b) a quadrilateral QRSP which has a common base QR with \(\Delta\)QRT such that QTP is a straight line, PQ || SR, |QP| = 9cm and |RS| = 4.5cm.

(i) Measure |PS| ; (ii) Find the perpendicular distance between RS and PQ ; (iii) What is QRSP?

Answer

Answer Details

(a) Construction of \(\triangle QRT\)

Draw \(QR=8\text{ cm}\).
With centre \(Q\) and radius \(4.5\text{ cm}\), draw an arc.
With centre \(R\) and radius \(6\text{ cm}\), draw an arc cutting the first arc at \(T\).
Join \(QT\) and \(RT\).

(b) Construction of \(QRSP\)

Produce \(QT\) through \(T\), and mark \(P\) on it such that \(QP=9\text{ cm}\).
Through \(R\), construct a line parallel to \(QP\). Mark \(S\) on this line so that \(RS=4.5\text{ cm}\).
Join \(P\) to \(S\). Drop \(RK\perp PQ\), where \(K\) lies on \(PQ\).

(i) From the construction, \[|PS|=6.0\text{ cm}.\]

(ii) The perpendicular distance between \(RS\) and \(PQ\) is \(RK\): \[RK=5.9\text{ cm}.\]

(iii) \(PQ\parallel RS\), while \(PQ=9\text{ cm}\) and \(RS=4.5\text{ cm}\). Thus, \(QRSP\) is a trapezium.

Using a ruler and a pair of compasses only, construct (a) triangle QRT with |QR| = 8cm, |RT| = 6cm and |QT| = 4.5cm. (b) a quadrilateral QRSP which has a co...