Correct the definition of triangle inequality to not include degenera…

exercises/triangle/description.md

@@ -2,6 +2,27 @@ The program should raise an error if the triangle cannot exist.
 
 ## Hint
 
-The sum of the lengths of any two sides of a triangle always exceeds or 
-is equal to the length of the third side, a principle known as the _triangle
-inequality_.
+The triangle inequality theorem states:
+z ≤ x + y
+where x,y, and z are the lengths of the sides of a triangle. In other words, the
+sum of the lengths of any two sides of a triangle always exceeds or is equal to
+the length of the third side.
+
+A corollary to the triangle inequality theorem is there are two classes of
+triangles--degenerate and non-degenerate. If the sum of the lengths of any two
+sides of a triangle is greater than the length of the third side, that triangle
+is two dimensional, has area, and belongs to the non-degenerate class. In
+mathematics, a degenerate case is a limiting case in which an element of a class
+of objects is qualitatively different from the rest of the class and hence
+belongs to another, usually simpler, class. The degenerate case of the triangle
+inequality theorem is when the sum of the lengths of any two sides of a triangle
+is equal to the length of the third side. A triangle with such qualities is
+qualitatively different from all the triangles in the non-degenerate class since
+it is one dimensional, looks like a straight line, and has no area. Such
+triangles are called degenerate triangles and they belong to the degenerate
+class.
+
+## Dig Deeper
+
+This exercise does not test for degenerate triangles. Feel free to add your own
+tests to check for degenerate triangles.