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
Quadrilateral directly from the quadrilateral identity formula_50 The sides "a", "b", "c", and "d" of any quadrilateral satisfy and Among all quadrilaterals with a given perimeter, the one with the largest area is the square. This is called the "isoperimetric theorem for quadrilaterals". It is a direct consequence of the area inequality where "K" is the area of a convex quadrilateral with perimeter "L". Equality holds if and only if the quadrilateral is a square. The dual theorem states that of all quadrilaterals with a given area, the square has the shortest perimeter. The quadrilateral with given side lengths that has