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ABCD is a parallelogram in which AB || CD
And non parallel sides AD and BC are equal.

Draw a line CE parallel to AD
CE || AD and AE || CD
Therefore, AECD is a parallelogram
angle CDA = angle CEA  (opp angles of ||gm)
AD = CE (opp sides of ||gm)
But AD = BC (given)
Therefore,  CE = BC
angle CEB = angle CBE (opp angles of equal sides)
angle CEB + angle CEA = 180⁰

angle CEB + angle CDA = 180⁰

Trapezium is cyclic as the sum of the pair of oppo angles is 180⁰.