Consider a pentagram (see picture below). There are 5 disjoint triangles initially.Just count the five 'caps' above the pentagon, do not count the larger triangles formed by using three of the 5 vertices, for those 'triangles' have lines going thru them. By adding just two lines, you can go from 5 to 10 disjoint triangles. How? (submitted by Bruce Lin, from friends at MIT, who got it from Andrew Russell, a graduate student in EE at MIT, who either made it up or got it from...?).