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2014-08-15T05:57:26+05:30

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Let BAC be Ф.   in ABC, B = C as isosceles Δ. 
ABC = BCA = (180 - Ф)/2 = 90-Ф/2

As AB parallel to CD,  BAC = ACD = Ф.
Also ACB = CAD  =  90 - Ф/2 

In ΔCAD,  ADC = 180 - ACD - CAD = 180 - Ф - 90 + Ф/2  = 90 -Ф/2
So ADC = ABC. 
Opposite angles are same and two sides are parallel,  it is a parallelogram

 
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