Triangle Inequality Modulus

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.

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!

a triangle worksheet with the measurements for triangles and their corresponding numbers on it
a triangle worksheet with the measurements for triangles and their corresponding numbers on it

Triangle Inequality Module

Triangle Inequality Theorem Discovery Activity 7.G.A.2

Triangle Inequality: Discovery Lesson

The Triangle Inequality
The Triangle Inequality
Triangle Inequality Theorem Worksheet
Triangle Inequality Theorem Worksheet

Triangle Inequality Module

Triangle inequality theorem

11 Triangle Inequality Theorem Activities That Rock - Idea Galaxy
11 Triangle Inequality Theorem Activities That Rock - Idea Galaxy
Triangle Inequality Theorem Discovery Activity 7.G.A.2
Triangle Inequality Theorem Discovery Activity 7.G.A.2

Triangle Inequality Theorem - fun with licorice - geometry activity

Triangle Inequality Module

Free Triangle Inequality Theorem foldable for Geometry Classroom

Students will explore the triangle inequality theorem by trying to create their own triangles with various side lengths. Students will cut out strips of paper to represent the side lengths of the triangles, then will put a given three together to test and see if a triangle can be formed.

Triangle Inequality: Discovery Lesson
Triangle Inequality: Discovery Lesson
Worksheet Triangle Inequalities
Worksheet Triangle Inequalities
Triangle Worksheets
Triangle Worksheets
Geometry Triangle Inequality Theorem Activity and Problems
Geometry Triangle Inequality Theorem Activity and Problems
Triangle Inequality Theorem Foldable
Triangle Inequality Theorem Foldable
Triangle Inequality Theorem ~ Discovery Activity and Practice
Triangle Inequality Theorem ~ Discovery Activity and Practice
Triangle Inequality Theorem 1, 2 and 3 Cheat Sheet!
Triangle Inequality Theorem 1, 2 and 3 Cheat Sheet!
Proofs without words
Proofs without words
Geometry Worksheets | Triangle Worksheets
Geometry Worksheets | Triangle Worksheets
two people standing on the edge of a large piece of paper that is shaped like a triangle
two people standing on the edge of a large piece of paper that is shaped like a triangle

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The Triangle Inequality Theorem Worksheets

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