Projective Geometry Math 5130 2 Suppose two quadrangles P QR

Projective Geometry Math 5130

(2) Suppose two quadrangles P QRS and P QRS are perspective from a point, i.e., P P , QQ , RR , SS are concurrent. Must the points of intersection of corresponding six sides must be collinear?

Solution

Yes they should be equal

Reason consider two cones and join them at their vertices ,such that there axis are same.

Let the first points lie on the base circumference of one cone then we can construct 2nd cone such that p\'q\'r\'s\' lies on it.

The vertex intersection point is intersection of the six plane.