How to Use the Triangle Inequality Theorem

Miacademy & MiaPrep Learning Channel

This educational math video provides a comprehensive guide to the Triangle Inequality Theorem, a fundamental concept in geometry. The narrator, Justin, begins by connecting the theorem to the Segment Addition Postulate, visually demonstrating how moving a point off a line segment creates a triangle and changes the relationship between lengths from equality to inequality. The video explains that for any triangle, the sum of any two side lengths must always be greater than the third side length. The content moves into practical application with multiple examples. Students learn how to test sets of three numbers to determine if they can form a valid triangle. The video covers scenarios where the inequality holds true, as well as cases where it fails (including an example where the sum equals the third side, resulting in a flat line rather than a triangle). The step-by-step walkthroughs emphasize checking all three possible combinations of sides to ensure validity. Finally, the lesson advances to finding the possible range for an unknown third side of a triangle given two known sides. The video derives the algebraic inequalities and then introduces a helpful shortcut: the length of the third side must be greater than the difference and less than the sum of the two known sides. This resource is highly valuable for geometry students as it bridges the gap between conceptual understanding and procedural skill, offering clear visuals and note-taking prompts throughout.