Triangle Inequality Theorem Worksheets

What is Triangle Inequality Theorem? 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 the triangle inequality theorem. The triangle inequality theorem 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.