Let be a convex pentagon with all five sides equal in length. The diagonals and meet in with . Prove that has a pair of parallel sides.
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Let $ABCDE$ be a convex pentagon with all five sides equal in length. The diagonals $AD$ and $EC$ meet in $S$ with $\angle ASE = 60^\circ$. Prove that $ABCDE$ has a pair of parallel sides.
Izvor: Srednjoeuropska matematička olimpijada 2011, ekipno natjecanje, problem 5
Školjka 
be a convex pentagon with all five sides equal in length. The diagonals 
and 
meet in 
with 
. Prove that