Draw parallelogram ABCD so sides AB // CD; AC // BD; and diagonals AD and BC intersect at point O.
Then side AB = side CD since opposites sides of a parallelogram are equal.
Angle DCO = Angle ABO since alternate interior angles formed by the transversal BC intersecting the parallel lines AB and CD are equal Angle
CDO = Angle BAO since alternate interior angles formed by the transversal BC intersecting the parallel lines AB and CD are equal
Triangles ABO and CDO are congruent by Angle Side Angle
CO=OB and AO =OD because sides opposite equal angles of congruent triangles are equal.
CB bisects AD and AD bisects CB by definition of bisection.
