MathDB
Parallelograms

Source: 2020 Latvia TST Round 1

March 30, 2020
geometryparallelogram

Problem Statement

It is given parallelogram ABCDABCD. On it's sides AB,BC,CD,DAAB, BC, CD, DA are chosen points E,F,G,HE, F, G, H such that area of EFGHEFGH is half of the area of ABCDABCD. Show that at least one of the quadrilaterals ABFHABFH and AEGDAEGD is parallelogram.
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