Geometry Problem 169. Parallelogram, Interior and Exterior Points, 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 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.
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