7th Grade · Geometry
Valid Triangle
7.G.A.2
Definition
A triangle whose side lengths satisfy the Triangle Inequality Theorem (the sum of any two sides exceeds the third). All three checks must pass.
Examples
- Sides 5, 8, 10: 5+8=13>10, 5+10=15>8, 8+10=18>5 — all pass, valid triangle.
- Sides 4, 6, 7: check smallest pair 4+6=10>7 — valid.
Key rule
If the shortest two sides sum to more than the longest side, it's valid — only need to check once.
Memory hook
Smallest two sides beat the biggest one? Valid.