Using ruler and compasses only, construct a quadrilateral ABCD in which AB = 6 cm, BC = 5 cm, ∠B = 600, AD = 5 cm and D is equidistant from AB and BC. Measure CD.

Following are the steps of Construction:

(i) Construct \[AB\text{ }=\text{ }6\text{ }cm.\]

(ii) At point B, construct angle 60⁰ and cut off

\[BC\text{ }=\text{ }5\text{ }cm\]

(iii) Construct the angle bisector of ∠B.

(iv) Taking A as centre and 5 cm radius construct an arc which intersects the angle bisector of ∠B at D.

(v) Now join AD and DC.

Here ABCD is the required quadrilateral.

By measuring \[CD\text{ }=\text{ }5.3\text{ }cm.\]