Well if two lines are cut by a transversal from the 2 sides (in quebec we call it a médiane) then look if the alternate interior angles are congruent after you if the lines are parallel. Also I think you souldve had study the 5 theorems to prove that lines are parallel lol.
For all quadrilaterals such that the approximate visual representation of said shape resembles that of a parallelogram, then that shape is a paralologram if and only if it is a paralologram