 Parallelogram

A parallelogram is the convex set with vertices $p,p+u,p+v,p+u+v$ for two linearly independent planar vectors $u,v$. Its opposite edges are parallel and its centre $p+(u+v)/2$ gives central symmetry. Its area is $|\det [u,v]|$, so an invertible linear map changes its area by the absolute value of that map's determinant. These facts make parallelograms convenient convex bodies for two-dimensional applications of the Minkowski convex body theorem.

A parallelogram is a four-sided polygon (quadrilateral) with two pairs of parallel sides. The opposite sides are not only parallel but also equal in length, and the opposite angles are equal. Some key properties of parallelograms include: 1. **Opposite Sides:** Both pairs of opposite sides are equal in length. 2. **Opposite Angles:** Both pairs of opposite angles are equal in measure.