Exercise 2, § 9

Let E be an affine space over a field of characteristic $\neq 2$ and $a, b, c, d$ any four points of E. Show that if $x, y, z, t$ are the respective midpoints of the ordered pairs $(a, b), (b, c), (c, d), (d, a)$, the quadruple $(x, y, z, t)$ is a parallelogram (Exercise 1).*