Geometry Problem 168. Parallelogram, Diagonals, Pentagon, Triangles, Areas. Level: High School, Honors Geometry, College, Mathematics Education

In the figure below, ABCD is a parallelogram with E an exterior point. Lines AE and DE and diagonals AC and BD determine the shaded regions of areas S1, S2, S3, S4, S5, and S6. Prove that S5 + S6 = S1 + S2 + S3 + S4.
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