7th Grade · Geometry
Range of the Third Side
7.G.A.2
Definition
Given two sides a and b, the third side c must satisfy |a - b| < c < a + b. This range ensures the Triangle Inequality is satisfied.
Examples
- Sides a=5, b=9: lower bound |5-9|=4, upper bound 5+9=14, so 4 < c < 14.
- c cannot equal 4 or 14 (open circles) — those are degenerate or impossible.
Key rule
The third side must be strictly between |a-b| and a+b, not equal to either.
Memory hook
Third side has to fit between a gap and a sum.