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The each diagonal of an irregular parallelogram divides the parallelogram in two equal and congruent parts. The diagonal bisects each other.
It means, if a irregular parallelogram rotates 180° about the midpoint of its diagonal, then the image of the parallelogram coincide with its preimage during the rotation.
If a irregular parallelogram rotates 360° about the midpoint of its diagonal, then the image of the parallelogram coincide 2 times with its preimage during the rotation.