Vectors of polygon sides

Given a polygon with vertices $A_1, A_2, ..., A_n$ in order, the vector of the side from $A_i$ to $A_{i+1}$ is $\vec{A_iA_{i+1}} = \overrightarrow{A_{i+1}} - \overrightarrow{A_i}$, where $\overrightarrow{A_i}$ is the position vector of $A_i$.

Important properties

• The sum of all side vectors of a closed polygon is the zero vector: $\vec{A_1A_2} + \vec{A_2A_3} + ... + \vec{A_nA_1} = \vec{0}$.

• Each side vector shows both the length and the direction from one vertex to the next.

• Side vectors can be used to calculate perimeter, check if a polygon is closed, and find other properties.