In the convex pentagon
the sides
are equal. Moreover each diagonal of the pentagon is parallel to a side (
is parallel to
,
is parallel to
etc.). Prove that
is a regular pentagon.
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In the convex pentagon $ABCDE,$ the sides $BC, CD, DE$ are equal. Moreover each diagonal of the pentagon is parallel to a side ($AC$ is parallel to $DE$, $BD$ is parallel to $AE$ etc.). Prove that $ABCDE$ is a regular pentagon.