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Draw BE//AD.
Therefore ABED is a Parallelogram
AD=BC (given) and
AD=BE(opposite sides of a parallelogram)
Therefore BC=BE
hence BCE is an isosceles triangle
therfore angleBCE=angleBEC ....(1)
angleADC + angleBEC= 180 (adjacent sides of a parallelogram is 180) ...(2)
angleBCD+angleBCE=180 (Linear pair) .....(3)
substituting  (1) in (3)
anldeBCD+anlgeBEC=180 ......(4)
from (1) and (4)
angle ADC=anlgeBCD
that is angle D=anlgeC ...(5)
angleA+angleD=180 (angles on the same side of transversal) ....(6)
angleB+angleC=180 ('' '') ...(7)
from (5) (6) and(7)
angle A= angle B
hence proved 
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