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: Discovery Lesson
Proves Inequalities In A Triangle
Triangle inequality theorem
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Proving Inequalities In A Triangle Module
Get students real world practice with the triangle inequality theorem with these 11 activity ideas. Includes print and go resources, discovery learning, online math tools, challenge questions, and more. Check it out!
Triangle Inequality Theorem Discovery Activity 7.G.A.2
How To Do Triangle Inequality
Inequalities in 1 Triangle: Dynamic & Modifiable Applet
A Geometry Theorem Looking for a Geometric Proof – David Richeson: Division by Zero
