Question

Using ruler and compasses only, construct a parallelogram ABCD, in which : AB = 6 cm, AD = 3 cm and $\angle$ DAB = 60${}^{\circ }$. In the same figure draw the bisector of angle DAB and let it meet DC at point P. Measure angle APB.

Answer 1

Steps :

1. Draw AB = 6 cm.
2. At A draw $\angle$ QAB = 60${}^{\circ }$.
3. From AQ cut AD = 3 cm.
4. From D, draw an arc of radius 6 cm.
5. From B, draw an arc of radius 3 cm which meets first arc at C.
6. Join CD and BC.
Thus ABCD is the required ||gm.
7. Bisect $\angle$ DAB, so that bisector meets CD at P.
8. Join PB and measure ZAPB.
$\therefore \angle APB={90}^{\circ }.$