Editing Parallelogram (section)

==Other properties==

*Opposite sides of a parallelogram are parallel (by definition) and so will never intersect.
*The area of a parallelogram is twice the area of a triangle created by one of its diagonals.
*The area of a parallelogram is also equal to the magnitude of the [[vector cross product]] of two [[adjacent side (polygon)|adjacent]] sides.
*Any line through the midpoint of a parallelogram bisects the area.<ref>Dunn, J.A., and J.E. Pretty, "Halving a triangle", ''Mathematical Gazette'' 56, May 1972, p. 105.</ref>
*Any non-degenerate [[affine transformation]] takes a parallelogram to another parallelogram.
*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]].
*The perimeter of a parallelogram is 2(''a'' + ''b'') where ''a'' and ''b'' are the lengths of adjacent sides.
*Unlike any other convex polygon, a parallelogram cannot be inscribed in any triangle with less than twice its area.<ref>{{cite web|last=Weisstein|first=Eric W|title=Triangle Circumscribing|url=http://mathworld.wolfram.com/TriangleCircumscribing.html|work=Wolfram Math World}}</ref>
*The centers of four squares all constructed either internally or externally on the sides of a parallelogram are the vertices of a square.<ref name=Weisstein>Weisstein, Eric W. "Parallelogram." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Parallelogram.html</ref>
*If two lines parallel to sides of a parallelogram are constructed [[concurrent lines|concurrent]] to a diagonal, then the parallelograms formed on opposite sides of that diagonal are equal in area.<ref name=Weisstein/>
*The diagonals of a parallelogram divide it into four triangles of equal area.