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