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.
Proves Inequalities In A Triangle
Triangle inequality theorem
Triangle Inequality Theorem Discovery Activity 7.G.A.2
Proof Of Triangle Inequality Theorem
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!
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.
Proof Of Triangle Inequality
Free Triangle Inequality Theorem foldable for Geometry Classroom
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