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4 triangles with equal areas, prove MNPQ parallelogram

Source: IGO 2015 Elementary 4

July 22, 2018
geometryareasparallelogramrectangle

Problem Statement

In rectangle ABCDABCD, the points M,N,P,QM,N,P, Q lie on ABAB, BCBC, CDCD, DADA respectively such that the area of triangles AQMAQM, BMNBMN, CNPCNP, DPQDPQ are equal. Prove that the quadrilateral MNPQMNPQ is parallelogram.
by Mahdi Etesami Fard
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