Using ruler and a pair of compasses only…

Question 1 Report

Using ruler and a pair of compasses only, construct:

(a) (i) quadrilateral PQRS with |PQ| = 6 cm, |PS| = 8 cm, < PSR = 90\(^o\), |SR| = 12 cm and |QR| = 11 cm;

(ii) perpendicular from Q to cut \(\over{SR}\) at K.

(b) Measure:

(i) IQRI;

(ii) < QRS.

Answer

Answer Details

(a) Construction

Draw the line segment \(SR=12\text{ cm}\).
At \(S\), construct a perpendicular to \(SR\). Mark \(P\) on it so that \(PS=8\text{ cm}\).
With centre \(P\) and radius \(6\text{ cm}\), draw an arc. With centre \(R\) and radius \(11\text{ cm}\), draw another arc cutting the first at \(Q\).
Join \(PQ\) and \(QR\) to complete quadrilateral \(PQRS\).
Construct the perpendicular from \(Q\) to \(SR\), meeting \(SR\) at \(K\).

(b) Measurements from the construction

(i) \(\lvert RK\rvert \approx 9.3\text{ cm}\).

(ii) \(\angle QRS \approx 55^\circ\).

Using ruler and a pair of compasses only, construct: (a) (i) quadrilateral PQRS with |PQ| = 6 cm, |PS| = 8 cm, < PSR = 90\(^o\), |SR| = 12 cm and |QR| = 11 ...