Here's one question that has been bothering me now for a while. It is not homework.
For an isosceles trapezoid (wikipedia link: http://en.wikipedia.org/wiki/Isosceles_trapezoid), do we always have that sum of the two diagonals is larger (or equal) than sum of the two bases? No matter how we choose the legs and the bases?
I tried this for many examples on the plane and it always seemed to be right (if my calculations were correct) and intuitively it seems to be correct. How would one go about proving this claim if its true? And if it isn't, does someone have a counter-example in mind?
Thanks for all the input in advance.