Question

Mark (✓) against the correct answer in each of the following:
In the given figure, ​∠B < ​∠A and ​∠D > ​∠C. Then
(a) AD > BC
(b) AD = BC
(c) AD < BC
(d) AD = 2BC

Answer 1

(c) AD < BC

In $△$AOB,
$\angle$B < $\angle$A
So, AO < BO .........(i)
(Side opposite the larger angle is larger)
In $△$DOC,
$\angle$C < $\angle$D
So, DO < CO .........(i)
(Side opposite the larger angle is larger)
Adding equations (i) and (ii), we get:
AO + DO < BO + CO
Therefore, AD < BC.