Demystifying Triangle Inequality

This is the first part of  the Triangle Inequality Series.


Given three segments, how are we sure that they will form a triangle?

Will the segments with lengths 3, 4, and 8 units form a triangle? What about 3, 5, and 8?

What conditions with respect to segment lengths must be satisfied, so that three segments form a triangle?

Shown below are the segments with lengths 3, 4 and 8 units. In the following illustrations, squares are used to clearly indicate the segments’ lengths.  Each square has side 1 unit.  As we can see, we cannot form a triangle if the sum of the lengths of the two sides is less than the third side.

Figure 1

Let us now examine a triangle with side lengths 3, 5, and 8 units. Referring to Figure 2, the sides will only be coinciding and will never meet when rotated outward as shown. » Read more