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
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
Triangle inequality theorem
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Inequalities in 1 Triangle: Dynamic & Modifiable Applet
Free Triangle Inequality Theorem foldable for Geometry Classroom
This card sort activity is the perfect way for High School geometry students to review the triangle inequality theorem and the Pythagorean theorem. This card sort activity requires students to use the Triangle Inequality Theorem, Converse of the Pythagorean Theorem, and Pythagorean Inequality Theorems to classify triangles as Acute, Obtuse, Right, or Not a Triangle when given 3 side lengths. This high school geometry activity is so much more fun than a regular free geometry worksheet.
The Triangle Inequality Theorem Worksheets
This performance task activity for the triangle inequality theorem from Illustrative Mathematics gives students real world applications. Check out all 11 activities for triangle inequality theorem.