1. When the diagonals bisect each other, it creates to equal length sides. 2. By the vertical angle theorem, the angles across from each other are congruent. 3. Thus, by SAS, the two triangles opposite to each other in a parallelogram are congruent. 4. The triangles are congruent, then all of the opposite sides and angles are congruent. 5. If all of the opposite sides and angles are congruent, then it is a parallelogram.