# In Fig. 7.49, ∠B < ∠A and ∠C < ∠D. Show that AD < BC.

**Solution:**

Given: ∠B < ∠A and ∠C < ∠D

To prove: AD < BC

We can use the fact that in any triangle, the side opposite to the larger (greater) angle is longer.

In ΔAOB, ∠B < ∠A (given)

AO < OB (The side opposite to the smaller angle is smaller) ... (1)

In ΔCOD, ∠C < ∠D

OD < OC (The side opposite to the smaller angle is smaller) ... (2)

On adding Equations (1) and (2), we obtain

AO + OD < BO + OC

AD < BC

Hence, proved

**Video Solution:**

## In Fig. 7.49, ∠B < ∠A and ∠C < ∠D. Show that AD < BC.

### NCERT Maths Solutions Class 9 - Chapter 7 Exercise 7.4 Question 3:

**Summary:**

If in the given figure, ∠B < ∠A and ∠C < ∠D, we have seen that AD < BC.