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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