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Prove that ABCDE has a pair of parallel sides

Source: Middle European Mathematical Olympiad 2011 - Team Compt. T-5

September 6, 2011
symmetrygeometry

Problem Statement

Let ABCDEABCDE be a convex pentagon with all five sides equal in length. The diagonals ADAD and ECEC meet in SS with ∠ASE=60∘\angle ASE = 60^\circ. Prove that ABCDEABCDE has a pair of parallel sides.
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