Answer :

Consider quadrilateral ABCD as shown where

AD = BC and AB = CD

∠ADC = ∠ABC = x

∠DAB = ∠BCD = y

For quadrilateral ABCD to be a parallelogram we need to prove that opposite sides are parallel i.e. AB || DC and AD || BC

Sum of all angles of a quadrilateral is 360°

⇒ ∠ADC + ∠ABC + ∠DAB + ∠BCD = 360°

⇒ x + x + y + y = 360°

⇒ 2x + 2y = 360°

⇒ x + y = 180°

Thus AB || DC and AD || BC

As opposite sides are congruent and parallel quadrilateral ABCD is a parallelogram

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