Math
Triangle inequality.
Definition
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This rule determines whether three given lengths can form a valid triangle.
Examples
Real-world.
- 1 Sides of 3, 4, and 5 form a triangle because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3
- 2 Sides of 1, 2, and 10 cannot form a triangle because 1 + 2 = 3 < 10
- 3 Determining the possible range for the third side of a triangle when two sides are 6 and 9: the third side must be between 3 and 15
Key Fact
For any triangle with sides a, b, c: a + b > c, a + c > b, and b + c > a