Home/Seventh Grade Math/Week 24: Angles and triangles/Lesson 6

Triangle Inequality

A triangle forms only when the sum of any two side lengths is greater than the third side.

Lesson 6

Concept

Triangle inequality conditions: For sides a, b, c: - a + b > c - a + c > b - b + c > a If any condition fails, no triangle exists. Example: 3, 4, 8 -> 3+4=7 not greater than 8, so not a triangle. Example: 5, 6, 8 -> all pair sums exceed third, so triangle exists.

Try it

Decide if each set can form a triangle: 1. 4, 5, 9 2. 7, 10, 12 3. 3, 3, 5 4. 6, 14, 7 5. 9, 11, 18 6. Give one possible third side if two sides are 6 and 8.