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see the attached figure , given , AB = CD AD = BC to prove that : ABCD is a IIgram proof :- AB = CD (from the given ) BC = AD (from the given ) BD = BD (common side ) ∴ Δ ADB ≡ Δ DBC by SSS congruence rule . therefore from CPCT we can write that ∠ADB = ∠ DBC (alternate interior angle ) since the alternate interior angles and opposite sides are equal in a quadrilateral therefore it is a IIgram . i hope it helps ...........................^_^

In quadrilateral ABCD AB=DC and AD=BC LET US construct diagnol AC and BD in triangle ACB and triangle ADC AB=DC(given) AC=AC(common side) BC=AD(common side) by SSS postulate triangle ADC is congruent to triangle BCA therefore angle BAC =angle BCA there fore AB||BC ..................FULL ANSWER IN PICTURE.....