Answer:
Theorem : Opposite sides of a parallelogram are congruent or equal.
Let us suppose a parallelogram ABCD.
Given:AB\parallel CD and BC\parallel AD (According to the definition of parallelogram)
We have to prove that: AB is congruent to CD and BC is congruent to AD.
Prove: let us take two triangles, \bigtriangleup ACD and\bigtriangleup ABC
In these two triangles, \angle1=\angle2 { By the definition of alternative interior angles}
Similarly, \angle4=\angle3
And, AC=AC (common segment)
By ASA, \bigtriangleup ACD \cong \bigtriangleup ABC
thus By the property of congruent triangle, we can say that corresponding sides of \bigtriangleup ACD and \bigtriangleup ABC are also congruent.
Thus, AB is congruent to CD and BC is congruent to AD.
