AD=BC and AD||BC.Is AB=DC?Give reasons in support of your answer.

Consider the figure,

In $∆ABC and ∆ADC$
AD = BC   (Given)
AC = AC  (Common)
$\angle ACB=\angle CAD$  (Alternate interior angles)
So, by SAS congruency rule
$∆CBA\cong ∆ADC$
Thus,
AB = DC  (c.p.c.t)

Therefore, AB = DC