Hi -

Desargues's Theorem says that if two triangles are drawn in perspective from a point, then the points of intersection of their corresponding pairs of sides are collinear.

To solve your problem, we need to end up with a diagram like the one attached.landmare the two initial lines and P is the given point. Triangles ABP and FGH are the ones that will end up being in perspective from the point of intersection off the paper. The dotted linenis the one we need to find, and the linekrepresents the line joining pairs of corresponding sides.

To draw the diagram, draw the given lineslandm, and the point P. Then the linek(more or less anywhere); then the other points in alphabetical order. Start with A and B in arbitrary positions on the linesmandl. This fixes C, D and E. Then choose any convenient point for F. Then find G and finally H. Join PH to find the linen.

Hope that helps.

Grandad