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.
Teach it
Where it is taught, with guided notes, practice, homework, an exit ticket and an interactive Teacher Deck.
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.