In addition the intersection-points of the corresponding line pairs M(EF,DC), O(DA,EB), N(AF,BC) are collinear (this is a special case of Pappus theorem).

To prove the first claim consider:

Line-bundle at E: EC/CA= ED/DK because of blue parallels.

Line-bundle at F: BG/BA = ED/DK because of green parallels.

Hence from the parallelity of blue line-pair and green line-pair follows the parallelity of the red line-pair.

The intersection point O of the line pair {AD,EB} divides AD in ratio ED/AB, since triangles {DEO,ABO} are similar.

The intersection point O' of the line pair {AD,MN} divides AD in ratio DM/AN, since triangles {DO'M,AO'N} are similar.

But ED/AB = DM/AN since triangles {EMD,BNA} are also similar. Hence O coincides with O'. This shows the collinearity of the three points.

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