7th Grade · Geometry
Triangle Inequality Theorem
7.G.A.2
Definition
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If this fails, no triangle can be formed.
Examples
- Sides 5,7,9: 5+7=12>9, 7+9=16>5, 5+9=14>7 — valid triangle.
- Sides 2,3,8: 2+3=5 < 8 — fails, not a valid triangle.
Key rule
Check the sum of the two smaller sides against the largest side — that's the critical test.
Memory hook
Two sides together must beat the third.