### Theory:

A quadrilateral whose opposite sides are parallel in pairs is called a parallelogram.
Properties of a parallelogram
 The opposite sides of the parallelogram are of equal length in pairs. $$AB = DC$$ $$BC = AD$$ The opposite angles of a parallelogram are equal in size. $\sphericalangle$$$A =$$$\sphericalangle$$$C$$ $\sphericalangle$$$B =$$$\sphericalangle$$$D$$ The parallelogram divides at the intersection of the diagonal in half. $$BO = OD$$ $$AO = OC$$ The diagonal of parallelogram divides it into two equal triangles. Triangles $$ABC$$ and $$CDA$$ are equal. The sum of the angles on each side of the parallelogram is $$180$$ degrees.  $\sphericalangle$$$A +$$$\sphericalangle$$$D = 180$$ degrees The transverse angles at the diagonal are the same. $\sphericalangle$$$BAC =$$$\sphericalangle$$$ACD$$ $\sphericalangle$$$BCA =$$$\sphericalangle$$$CAD$$