#### Triangle Inequality Theorem tells us that if you add any two sides of a triangle, they will be greater than the third side in length. The basic reason is that if that third side was longer, the two sides would never meet up. This can help us mathematically determine if in fact you have a legitimate triangle. In fact this is calculation is being performed hundreds of times each second that your mobile phone is looking for a signal.

We all are familiar with the fact that we need three line segments to form a triangle. But what most of us don't know that the three line segments used to form a triangle need to have a relationship among themselves. For instance, if you were given lines segments of measurements 3, 4,5, you can easily form a triangle out of it. On the other hand, you cannot form a triangle out of measurements 3,4, and 9. Therefore, you cannot create a triangle from any three segments; you need the three line segments in a relationship. That relationship is explained by this theorem. It basically states that the length of any side of the triangle should be shorter than the sum of the two segments added together. This shows that for creating a triangle, no side can not be longer than the lengths of sides combined. For example, we can easily create a triangle from lengths 3, 4, and 5 as these lengths don't satisfy the theorem. 4 + 5 = 9 and 3 < 9 : 3 + 4 = 7 and 5 < 7 : 3 + 5 = 8 and 4 < 8 It is clear that none of the line segment is longer than the two sides of the triangle. However, if we considered lengths 3, 4, and 9, we know that length 9 is longer than the sum of the two sides. 3 + 4 = 7 and 9 > 7. These worksheets explain how to use inequalities to determine the length of a triangle's sides. Please remind students how this skill basically relates to all work with triangles.