Need to prove the theorem "if opposite angles of a quadrilateral are congruent, then its a parallelogram". It'll probably involve triangles, diagonals, cpctc, and then eventually alternate interior angles. I proved that if one pair of sides are congruent and parallel, opposite sides congruent, and that diagonals bisect each other...dunno why I can't manage this one lol.
Call one of the angles x, and the other angle y. 2x+2y = 360, because sum of all angles in a quadrilateral is 360 x+y = 180, therefore the two angles are supplementary And since the alternate interior angles are supplementary, the two opposite sides are parallel. QED
coolio julio. this answer was a bit more algebraic than the other ones. I was thinking of like triangles and stuff with their diagonals. thanks~!!!