Discover, state, and prove a theorem that compares the length of the longest side of a quadrilateral with the sum of the lengths of the other three sides.
I attempted by first drawing a diagonal connecting two vertices of the quadrilateral, and attempting to use the triangle inequality theorem to relate the largest side with the sum of the lengths of the others. I end up with the two equations, A + D > E and B + C > E, and after adding them together, I end up with:
A + B + C + D > 2E,
where A is the longest side, B, C, D are the other sides, and E is the diagonal I drew. I don't know where to go from here.
Any help is appreciated.