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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)

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Solution

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


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