Parallelogram Parallelogram In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The
Tangential quadrilateral and sufficient condition is that a convex quadrilateral "ABCD" is tangential if and only if the incircles in the two triangles "ABC" and "ADC" are tangent to each other. A characterization regarding the angles formed by diagonal "BD" and the four sides of a quadrilateral "ABCD" is due to Iosifescu. He proved in 1954 that a convex quadrilateral has an incircle if and only if Further, a convex quadrilateral with successive sides "a", "b", "c", "d" is tangential if and only if where "R", "R", "R", "R" are the radii in the circles externally tangent to the sides "a", "b",