Exercise 1, § 9

In an affine space E over a field K, a quadruple $(a, b, c, d)$ of points of E is called a parallelogram if $b - a = c - d$, in which case $(a, d, c, b)$ is also a parallelogram. Show that if K is of characteristic $\neq 2$ the midpoints of the ordered pairs $(a, c)$ and $(b, d)$ are then equal; what can be said when K is of characteristic 2?*