### Parallelogram definition

A parallelogram is a quadrilateral that has two pairs of parallel sides.

The parallelogram has vertices at the points $\vc{a}$, $\vc{b}$, $\vc{c}$, and $\vc{d}$. We say it is spanned by the vectors $\vc{u}$ and $\vc{v}$. The point $\vc{e}$ is the midpoint between $\vc{a}$ and $\vc{d}$ as well as the midpoint between $\vc{b}$ and $\vc{c}$.