Question

In the given figure, $\angle B$ < $\angle A$ and $\angle C$ < $\angle D$. Then what's the relation between AD and BC?

(a) AD > BC

(b) AD = BC

(c) AD < 2BC

(d) AD < BC

[ 1 mark ]

Answer 1

In $\Delta$ AOB
$\angle B$ < $\angle A$
$\Rightarrow$ AO < BO
(side opposite to smaller angle is smaller) ... (1)

Now in $\Delta$COD
$\angle C$ < $\angle D$
$\Rightarrow$ OD < OC
(side opposite to smaller angle is smaller) ... (2)

[ 0.5 marks ]

On adding equations (1) and (2), we have
AO + OD < BO + OC
AD < BC

[ 0.5 marks ]