I'm not sure if I should've started a new thread for this but.. I need some help trying to prove that the diagonals of a parallelogram bisect each other.. I think I have an idea of how to solve this but I can't seem to put it together: Given AB = DC AD = BC Known AB + BC = AC BC + BD = BD and so forth.. I'm trying to prove that BZ = ZD and AZ = ZC. Using position vectors, I determined that the midpoint of vector AC to be OA + OB/2 = OZ and that AZ = OA - OZ and ZC = OZ - OC. I had the train of thought in my mind on how to persue this problem before but I lost it somehow after thinking too hard. I know these are the right steps that need to be considered to finish the problem, but in what steps do I need to do in order to finish this problem?