KöMaL 2020 C1633

Let $P$ be an interior point of one side of a unit square. Consider all parallelograms with one vertex at $P$, and one on each side of the square. Prove that if $P$ is not the midpoint of the side then $(i)$ there are exactly two rectangles among these parallelograms, and $(ii)$ the sum of the areas of these two rectangles is 1.