Check out these 11 activities to get students real world practice with the triangle inequality theorem. This post includes print and go resources, online math tools, challenge questions, and more. Check it out!
Triangle inequality theorem

Isosceles Triangle Inequality Theorem
Triangle Inequality Theorem (V1): Students can use this interactive applet to intuitively and informally discover this theorem.
The triangle inequality says a detour is never shorter than going straight. ‖u + v‖ ≤ ‖u‖ + ‖v‖ Equality holds exactly when u and v are parallel and point the same way; in the general case the direct vector u + v is strictly shorter than following u then v. The same statement reappears for real numbers as |a + b| ≤ |a| + |b| and for integrals as |∫f| ≤ ∫|f|, with the reverse form ‖u‖ − ‖v‖ ≤ ‖u − v‖ often the more useful of the two. This single inequality is what makes a distance a distance.


Triangle Inequality Theorem Worksheet
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