Parallelogram

Definition

A quadrilateral with two pairs of opposite sides that are each parallel to each other is called a parallelogram.

For two distinct vectors $\mathbf{a}$ and $\mathbf{b}$ on a 2-dimensional coordinate plane, the following set is called a parallelogram.

$$ R = \left\{ \lambda_{1}\mathbf{a} + \lambda_{2} \mathbf{b} : 0\leq \lambda_{1},\lambda_{2}\leq 1, \quad \mathbf{a} \ne \mathbf{b} \right\} $$

By definition, a parallelogram is also a trapezoid.

$\implies$ Rectangle $\implies$

$\implies$ Rhombus $\implies$