1. The problem statement, all variables and given/known data Let [tex]z_1[/tex], [tex]z_2[/tex], [tex]z_3[/tex] and [tex]z_4[/tex] be te position vectors of the vertices of quadrilateral AMCD. Prove that ABCD is a parallelogram if and only if [tex]z_1-z_2-z_3+z_4=0[/tex]. 2. Relevant equations 3. The attempt at a solution The solution obviously uses the fact that collinear vectors of equal magnitude are equal, but I get [tex]z_1-z_2+z_3-z_4=0[/tex]. Am I missing something obvious or is it just notations issue with the vertices of the quadrilateral.