Prove that opposite angles of a parallelogram are congruent. be sure to create and name the appropriate geometric figures.

Aparallelogram is by definition a quadrilateral whose opposite sides are parallel. we can define then two triangles containing the two angles of the parallelogram using the diagonal. the formed triangles then are congruent by the sss statement of congruent triangles (they have a common side and the two other sides are equal from the properties of a parallelogram).  now, since the two angles are corresponding, then the two angles are congruent.