It is shown that opposite angles are congruent - the ones marked with a double arc -. We can prove that the opposite sides are parallel:
Since angles in blue are congruent and are in each side of the same line, we can think of segment BD as a transversal and segments AB and CD would be the parallel lines:
These angles are called alternate interior angles.
SInce AB and CD are parallel and the angles with double arc are congruent, then the lines that form those angles with the paralles must be parallel too: AD//BC
