Consider four points I, K, H, J on the sides of the quadrangle and their images I* = T(I), ...etc. Joining the resulting points with lines one defines the quadrangle q* = LML*M*. It has indeed the property that opposite vertices are respectively images of one another through T. i.e. L* = T(L) , L = T(L*) etc. ...

The proof for L, L* follows from the fact that line IK, maps via T to I*K* and line HJ to H*J*. Thus, their intersection, which is L, maps to the corresponding intersection, which is L*. A similar argument shows also the collinearity of M, G and M*.

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