The Triangle Inequality
On this web page you will explore a relationship between the lengths of the three sides of a triangle.
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.
- Initially, how is the sum AC + CB related to the length of side AB?
- Does this relationship change when you drag the vertices of the triangle?
- Find a location for point C for which AC + CB = AB. Describe what happens to the triangle at this point.
- Formulate the Triangle Inequality Conjecture: The sum of the lengths of any two sides of a triangle is _____ the length of the third side.
- 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?