Cartesian Vectors and Quadrilaterals

[Starcrafty]

I have no clue where to start on this question.
Use Cartesian vectors in two-space to prove that the line segments joining midpoints of the consecutive sides of a quadrilateral form a parallelogram.

Atm all i can deduce from the information is that vectors 2A+2B+2C+2D=0 therefore midpoint vectors A+B+C+D=0 and to prove that it is a parallelogram A+B//C+D and vector A+C//B+D

 

[HallsofIvy]

Since this talks about using parallelograms, how about using the "parallelogram law" for vector addition? That is, that for vectors u and v, u+ v is the length of the longer diagonal of the parallelogram having u and v as sides and u- v is the length of the shorter diagonal.