Geometry Proof???????? Please Help!!!!?

Question

I need help with the following proof (If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram) Please help me with this proof ASAP. :) Thanks.

Please put this in a two column proof an give the reasons as well. Thanks you.

Answer 1

If adjacent angles add up to 180 degrees, then the sides that form those angles have to be parallel.

You know that opposite angles are equal to each other -- that is

A = C and B = D.

You also know that the four angles of a quadrilateral add up to 360 degrees.

So --

A+B+C+D = 360

By the identities above, we get"

A+B+A+B = 360

or

2A+2B = 360

Therefore

A+B = 180, so adjacent angles add up to 180, so the opposite sides are parallel.