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The figure below shows a quadrilateral ABCD. Points E, F, G, H, M, N, P, and Q trisect the sides (divide each side into three equal parts). Prove that EN and FM trisect QG and PH, respectively, similarly PH and QG trisect EN and FM.

Take ANY CONVEX QUADRILATERAL & trisect each of its sides. Then create this TIC-TAC-TOE board (as shown). How can we explain this surprising behavior? 😯🤔Source: @gogeometry. https://t.co/DUA6VDlODp @geogebra #MTBoS #ITeachMath #geometry #proof #PCTM19 #PCTM2019 #math #maths pic.twitter.com/TghLshmcra— Tim Brzezinski (@Brzezinski_Math) August 6, 2019

Take ANY CONVEX QUADRILATERAL & trisect each of its sides. Then create this TIC-TAC-TOE board (as shown). How can we explain this surprising behavior? 😯🤔Source: @gogeometry. https://t.co/DUA6VDlODp @geogebra #MTBoS #ITeachMath #geometry #proof #PCTM19 #PCTM2019 #math #maths pic.twitter.com/TghLshmcra

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