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."
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!