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see the attached figure ,
given , 
AB = CD 
to prove that : ABCD is a IIgram
proof :- AB = CD (from the given )
              BC = AD (from the given )
              BD = BD (common side )
∴ Δ ADB ≡ Δ DBC by SSS congruence rule . 
therefore from CPCT we can write that ∠ADB = ∠ DBC (alternate interior angle )
since the alternate interior angles and opposite sides are equal in a quadrilateral therefore it is a IIgram . 
  i hope it helps ...........................^_^

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In quadrilateral ABCD
LET US construct diagnol AC and BD
in triangle ACB and triangle ADC
AC=AC(common side)
BC=AD(common side)
by SSS postulate
triangle ADC is congruent to triangle BCA
therefore angle BAC =angle BCA
there fore AB||BC
..................FULL ANSWER IN PICTURE.....
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