The theorem that if the opposite sides of a quadrilateral are equal, then it is a parallelogram does not seem to exclude the possibility [br]that the figure might cross over itself. Drag Points B or C around[br]in a circle to see this effect. Change the proportions of the figure [br]by dragging the sliders.[br][br]To rule out this interpretation, we should make it clear that the edges of a polygon meet only the adjacent edges, and only at the endpoints.

If a quadrilateral is a rectangle, the diagonals are equal. [br]The converse is not true. Move the yellow control points.