Question

Let ABCD be a quadrilateral in which AD is the largest side and BC is the smallest side. Prove that ∠A < ∠C. (Hint: Join AC)

Answer 1

Given: Quadrilateral ABCD with AD and BC as the longest and shortest sides

To Prove: ∠C > ∠A

Construction: Join AC

Proof:

We know that in a triangle, the angle opposite to the longest side is greatest.

In ΔADC:

∠5 > ∠1 … (1) (AD is the longest side)

In ΔABC:

∠6 > ∠2 … (2) (BC is the shortest side)

Adding (1) and (2):

∠5 + ∠6 > ∠1 + ∠2

∴∠C > ∠A