<P> Thus all parallelograms have all the properties listed above, and conversely, if just one of these statements is true in a simple quadrilateral, then it is a parallelogram . </P> <Ul> <Li> Opposite sides of a parallelogram are parallel (by definition) and so will never intersect . </Li> <Li> The area of a parallelogram is twice the area of a triangle created by one of its diagonals . </Li> <Li> The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides . </Li> <Li> Any line through the midpoint of a parallelogram bisects the area . </Li> <Li> Any non-degenerate affine transformation takes a parallelogram to another parallelogram . </Li> <Li> A parallelogram has rotational symmetry of order 2 (through 180 °) (or order 4 if a square). If it also has exactly two lines of reflectional symmetry then it must be a rhombus or an oblong (a non-square rectangle). If it has four lines of reflectional symmetry, it is a square . </Li> <Li> The perimeter of a parallelogram is 2 (a + b) where a and b are the lengths of adjacent sides . </Li> <Li> Unlike any other convex polygon, a parallelogram cannot be inscribed in any triangle with less than twice its area . </Li> <Li> The centers of four squares all constructed either internally or externally on the sides of a parallelogram are the vertices of a square . </Li> <Li> If two lines parallel to sides of a parallelogram are constructed concurrent to a diagonal, then the parallelograms formed on opposite sides of that diagonal are equal in area . </Li> <Li> The diagonals of a parallelogram divide it into four triangles of equal area . </Li> </Ul> <Li> Opposite sides of a parallelogram are parallel (by definition) and so will never intersect . </Li> <Li> The area of a parallelogram is twice the area of a triangle created by one of its diagonals . </Li>

A shape that has 2 sets of parallel sides and no right angles