Answer
In a parallelogram, by definition, opposite sides are parallel. Since the opposite sides are intersected by a common transversal, this means that alternate interior angles are congruent, meaning that the angles on the left side of the transversal are congruent, and the angles on the right side of the transversal are congruent. In addition, since the lower left angle and the lower right angle correspond to congruent arcs, it follows that these angles are congruent, meaning that all four angles are congruent. Since all four angles add to 360 degrees, this means that they are all 90 degree angles, making the parallelogram a rectangle.
