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ABCD is # if MENF is #

Source: 1st National Women's Contest of Mexican Mathematics Olympiad 2022 , level 1 p1

September 17, 2022
geometryparallelogram

Problem Statement

Let ABCDABCD be a quadrilateral, EE the midpoint of side BCBC, and FF the midpoint of side ADAD. Segment ACAC intersects segment BFBF at MM and segment DEDE at NN. If quadrilateral MENFMENF is also known to be a parallelogram, prove that ABCDABCD is also a parallelogram.
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