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If i have two triangles $EFG$ and $CBD$ in perspective the triangle, how can i show that $H = GE.CD$, $I=EB.CF$ and $J=GB.DF$ are colinear. Any hints?

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Tommy do Nascimiento
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1 Answers1

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Indeed one does not need the two triangles to be in perspective. Think of two triangles in $\mathbb R^3$, so that $C, D, E, G$ are in a plane and $B, F$ are not. Consider the plane $L_1$ containing $B, E, G$ and $L_2$ containing $C,D,F$. Then both planes contain $H, I, J$. Thus $H, I, J$ are collinear.