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ABCD is a parallelogram: AD base.  Now draw bisectors from B meeting CD in F and bisector from D meeting AB in E. 
 We have EAD =EDC = D/2    and  ABF = FBC = B/2
 remember B+C = 180 degress and also  C+D = 180
To prove BF & ED parallel 
           ie.,  EDC = D/2 = BFC  ie., ED & BF make same angle with CD.

angle BFC = 180 - C - B/2  =  B - B / 2 = B/2  or D/2           as angles B = D.
                                   =  angle EDC
So proved.