This problem turns out to be a Tough Nut though it is not hard! You are asked to prove that in every tetrahedron there is a vertex such that the three edges meeting there have lengths which could be the sides of a triangle.

Try a proof by contradiction and use the triangle inequality which says that a triangle can be constructed with 3 given segments for sides if and only if the sum of the lengths of any two exceeds the length of the third. (For example the lengths 2, 3 and 7 cannot make the sides of a triangle because