In quadrilateral ABCD, AB || CD and AD || BC. Prove that ∠ABC = ∠ADC.

Since AB || DC and AD is the transversal
⇒ ∠BAD + ∠ADC = 180°     …. (Consecutive interior angles) …(i)
Again AD || BC and AB is the transversal 
⇒ ∠DAB + ∠ABC = 180° ….(ii)
Comparing eqns (i) and (ii), we get
⇒ ∠BAD + ∠ADC = ∠DAB + ∠ABC
          .^.. ∠ADC = ∠ABC