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equal areas from midpoints of ABCD (2007 Estonia Open Junior 1.2)

Source:

March 27, 2020

equal areasmidpointsgeometryparallelogram

Problem Statement

The sides

AB, BC, CD

and

DA

of the convex quadrilateral

ABCD

have midpoints

E, F, G

and

H

. Prove that the triangles

EFB, FGC, GHD

and

HEA

can be put together into a parallelogram equal to

EFGH