Question

AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of ∠B and ∠D decide which is greater.

Answer 1

Given: In quadrilateral ABCD, AB is the smallest and CD is the largest side

To find: ∠B > ∠D or ∠D > ∠B.

Construction: Join BD.

Now, in ΔABD, AD > AB   ...[Since, AB is the smallest side in ABCD]

⇒ ∠1 > ∠3  [Angle opposite to larger side is greater]  ...(i)

In ΔBCD, CD > BC  ...[Since, CD is the largest side in ABCD]

⇒ ∠2 > ∠4   [Angle opposite to larger side is greater]  ...(ii)

On adding equations (i) and (ii), we get

∠1 + ∠2 > ∠3 + ∠4

Hence, ∠B > ∠D