In the figure below, ABCD is a parallelogram with E an exterior point and F an interior point. Lines EA, EB, EC, ED, FA, FB, FC, and FD determine the shaded regions of areas S1, S2, S3, S4, S5, and S6. Prove that S5 + S6 = S1 + S2 + S3 + S4. Post a comment or solution.