Video narration
Now try 2, 3, and 5. Two plus three equals five. The pencils line up, but they do not enclose a region. Equality gives a straight line. With 2, 3, and 6, two plus three is less than six, so the ends cannot even reach. Here is the quick version. Find the longest length. If the other two add to more than it, the triangle works. If they equal it or fall below it, it fails. Checking the longest side is enough because, with positive lengths, the other two pairwise checks are automatically satisfied. With two sides a and b, a third side c must fit between their difference and their sum: |a-b| < c < a+b. So, can three lengths make a triangle? Yes-only when the sum of any two sides is greater than the third.