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The Triangle Inequality

On this web page you will explore a relationship between the lengths of the three sides of a triangle.

Sketch

This sketch shows triangle ABC, the lengths of the sides, AB, AC, and CB, and the sum AC + CB. Drag any of the vertices to change the shape of the triangle. Observe how the measurements are related as you change the triangle.

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Investigate

  1. Initially, how is the sum AC + CB related to the length of side AB?
  2. Does this relationship change when you drag the vertices of the triangle?
  3. Find a location for point C for which AC + CB = AB. Describe what happens to the triangle at this point.
  4. Formulate the Triangle Inequality Conjecture: The sum of the lengths of any two sides of a triangle is _____ the length of the third side.
  5. It is often said that the shortest distance between two points is along the segment connecting them. How does the Triangle Inequality Conjecture support this statement?