# ABCD is a quadrilateral in which AB || DC and AD = BC. Prove that ∠A = ∠B and ∠C = ∠D.

Given, ABCD is a quadrilateral in which AB || DC and AD = BC.

Extend AB to E and draw a line CE parallel to AD.

Since AD||CE and transversal AE cuts them at A and E, respectively.

A + E = 180

A = 180-E

So quadrilateral AECD is a parallelogram.

Now, AD = CE BC = CE

In ΔBCE,

CE = BC

CBE = CEB (opposite angles of equal sides are equal)

180-B = E

180-E = B

A = B

Hence, proved.

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