Desargues' Theorem . Modern Geometry
B 7 B In the picture above, triangle AABC and triangle...
B 7 B In the picture above, triangle AABC and triangle AA'B'C' are perspective from the point X, where A' and C' are points at infinity not indicated in the picture, so this problem involves working in the projective plane. The lines XẢ and B’Ś are parallel in the affine plane (that is, they intersect at a point at infinity in the projective plane), and V is on B'Ś. The lines XĆ and B'R are parallel in the affine plane, and U and S are on XC and W is on B'Ř. Furthermore, the point B' is on XB, and U, V and W are on line AB. In other words, points and lines are as they appear to be.