In Fig., find the

From the figure:

x + 50^o = 180^o(Linear pair)

x = 180^o - 50^o

x = 130^o

y = 130^o(Vertically opposite angles)

Now,

x = y = 130^o(Alternate interior angles)

Hence,

The theorem says that when the lines are parallel, the alternate interior angles are equal. And thus, the lines must be parallel.

AB || CD

Hence, Proved.