Math Geometry • Basic Shapes and Properties
Check whether three side lengths can form a triangle using the Triangle Inequality Theorem. A triangle exists iff each pair sums to more than the third side.
Inputs accept 1e-3, pi, sqrt(2) etc. Use * for multiplication.
Degenerate means the “triangle” collapses into a straight line (area = 0).
Drag to pan • Wheel/trackpad to zoom • “Reset view” restores framing.
Three lengths form a non-degenerate triangle if and only if each pair sums to more than the third side: a + b > c, a + c > b, and b + c > a. Enter a, b, and c to have the calculator evaluate these conditions.
A degenerate triangle occurs when one inequality becomes an equality (or is extremely close), such as a + b = c. Geometrically, the triangle collapses into a straight line and has zero area.
If you sort the sides so s1 <= s2 <= s3, then it is enough to check s1 + s2 > s3. If that holds, the other two inequalities automatically hold as well.
Real measurements and rounding can make a + b look equal to c even when it is slightly different. The tolerance setting decides how close to equality counts as degenerate instead of valid or invalid.
No, the inequalities are scale-based and remain true under consistent unit changes. Units in the calculator are used to label the values you enter and the comparisons it reports.