Solutions for Lesson 7-3 Triangle Inequality Problems

To determine whether a set of three side lengths forms a valid shape, check if the sum of any two sides is greater than the third. This is the core principle behind this concept.

For example, given sides of lengths 3, 4, and 5, add 3 + 4 = 7, which is greater than 5, 4 + 5 = 9, greater than 3, and 3 + 5 = 8, greater than 4. Since all conditions are met, these values can form a shape.

In contrast, for sides of lengths 1, 2, and 5, 1 + 2 = 3, which is less than 5, so these values cannot form a valid shape. Always check each pair of sides to verify this rule.

Recheck your answers by applying these steps to different sets of numbers. It will help you understand the logic and apply it to more complex problems in the future.