# Prove or disprove the non colinearity of three points

Prove or disprove: Let $$ABCD$$ be a quadrilateral in Pasch Geometry for which the following holds $$AB\cap CD=\{E\}$$, $$AC\cap BD=\{F\}$$ and $$AD\cap BC=\{G\}$$. Then the points $$E,F,G$$ are not collinear.

I tried to prove by contradiction defining a graph on set $$\{A,B,C,D\}$$ with edge between two points if they lie on different sides of the line $$EFG$$ but couldn't arrive to a contradiction. Maybe there is a counterexample in Poincaré Geometry.

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