The difference between any two sides of a triangle is ________ the third side.

Let AB, BC and AC be the sides of the triangle.

We know that the sum of the length of any two sides of a triangle is always greater than the third side. This gives us:
AB < BC + AC   ...(i)
BC < AB + AC   ...(ii)
AC < AB + BC   ...(iii)

From equation (i):

Subtract BC from both sides, then AB - BC < AC

From equation (ii):

Subtract AC from both sides, then BC - AC < AB

From equation (iii):

Subtract AB from both sides, then AC - AB < BC

Therefore, we can conclude that the difference between the lengths of any two sides of a triangle is always less than the length of the third side.