Triangle Inequality Theorem

Learning Objectives State the Triangle Inequality Theorem in its three forms. Determine if three given side lengths can form a valid triangle. Calculate the possible range of lengths for the third side of a triangle when two sides are known. Apply the theorem to solve algebraic problems where side lengths are represented by expressions. Use the Triangle Inequality Theorem as a justification in geometric proofs. Connect the theorem to real-world problems involving distances and structural design. If you have two paths to get to a friend's house, one direct and one that goes via the library, which path is shorter and why? 🗺️ The Triangle Inequality Theorem gives us the mathematical answer! This tutorial explores the Triangle Inequality Theorem, a fundamental rule governi...

TermDefinitionExample TriangleA closed, two-dimensional shape with three straight sides and three angles.A shape with vertices at points A, B, and C is denoted as ΔABC. Side LengthThe length of one of the three line segments that form a triangle.In ΔABC, the side lengths are commonly denoted as a, b, and c, where 'a' is opposite angle A, 'b' is opposite angle B, and so on. InequalityA mathematical statement that asserts that two quantities are not equal. It uses symbols like > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).The statement 7 > 4 is an inequality. SumThe result obtained by adding two or more numbers together.The sum of the side lengths 5 and 8 is 13. Absolute DifferenceThe positive difference between two...

The Triangle Inequality Theorem (Sum Rule) For a triangle with side lengths a, b, and c: 1. a + b > c 2. a + c > b 3. b + c > a Use this to verify if a triangle can be formed from three given side lengths. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. All three conditions must be true. The Third Side Range Rule (Corollary) For a triangle with side lengths a, b, and c: |a - b| < c < a + b Use this to find the possible range of lengths for the third side (c) when you know the lengths of the other two sides (a and b). The third side must be greater than the difference of the other two and less than their sum.