1. The problem statement, all variables and given/known data Problem 55 from Kiselevś Geometry - Book I. Planimetry: "Prove that each diagonal of a quadrilateral either lies entirely in its interior, or entirely in its exterior. Give an example of a pentagon for which this is false." 2. Relevant equations 3. The attempt at a solution The pentagon part is pretty easy. I'm having trouble with the proof. A proof by contradiction seems to be the easiest way to solve this problem but I'd prefer a proof that also explains why this should be true. I've tried using straight line properties (i.e. a straight line can be formed though any two points and it is unique) but I haven't gottten anywhere. Thanks in advanced for any help!