Question

In a quadrilateral ABCD, suppose AB = CD and AD = BC. Prove that ABCD is a parallelogram.

Answer 1

Given: ABCD is a quadrilateral, where AB = CD and AD = BC.

To Prove: Quadrilateral ABCD is a parallelogram.

Proof: Join AC.

In ΔABC and ΔCDA:

Hence, from SSS congruency, we get ΔABC ≅ ΔCDA.

Similarly, .

Hence, quadrilateral ABCD is a parallelogram.