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Let $\triangle ABC$ and $\triangle A'B'C'$ be two triangles. The line through $A$ and perpendicular to $AA'$ meets the line through $B'$ and perpendicular to $BB'$ at $A_b$; The line through $A$ and ...

I am looking for a minimal number of properties describing a triangle so that these properties are invariant to the choice of a Cartesian coordinate system as well as to the order in which the ...