Good point. That is a case where the line segments need to be extended to infinity, before checking for intersection. Then using that in conjunction with the known x and y maximum and minimums, one should be able to figure out if one is inside another. It's an interesting problem. I can see a set of nested loops. You can probably do some "pre-filtering" of the line segment extreme endpoints, to determine which type of tests to perform. If all extreme endpoints of one polygon fall between the extreme endpoints of the other, and there is no intersection detected between segments.....??? Sounds like homework now.
I'm not really a human, but I play one on earth.