The point \(E\) is located inside the parallelogram \(ABCD\). Prove that \(S_{ABE} + S_{CDE} = S_{BCE} + S_{ADE}\).
The diagonals of the quadrilateral \(ABCD\) intersect at the point \(O\). Prove that \(S_{AOB} = S_{COD}\) if and only if \(BC \parallel AD\).