Parallelograms are a type of polygons which you can apply the vectors to calculate some of their elements (vertexes, sides, diagonals, midpoints,...) knowing others. For instance:

1) From one parallelogram ABCD give us three consecutive vertexes D, A and B, and it is asked the other vertex C, we can calculate it making one of the translations:

C = D + = D +
C = B + = B +

where we have used the fact that = and =, they make ABCD a parallelogram (we remember that =B–A and =D–A).

2) Also in the same previous conditions, that is to say, known three consecutive vertexes D, A and B, we can get the centre M of the parallelogram (that it is also the intersection of the diagonals) like midpoint of the segment BD, and later get C like a symmetrical of A respect to C.

3) From a parallelogram ABCD give us two consecutive vertexes A and B, and his centre M, we can get the other two vertexes C and D like symmetrical respective to A and to B respect to M.