Unit 4 · Triangle Foundations

4.4Triangle Inequality Theorem

Quick Answer

Triangle Inequality Theorem: the sum of any two side lengths of a triangle must be greater than the third side length. Check all three combinations: a+b>c, a+c>b, b+c>a.

Essential Question

What constraint do the Triangle Inequality Theorem place on the side lengths of a triangle, and how do we use it to test whether three lengths can form a triangle?

Learning Goals

  • 1State the Triangle Inequality Theorem.
  • 2Test whether three lengths can form a triangle.
  • 3Find the range of possible lengths for a third side.
  • 4Apply the theorem to real-world problems.

Key Vocabulary

Triangle Inequality Theorem

The sum of any two side lengths of a triangle must be greater than the third side length.

Range of the third side

If two sides have lengths a and b, the third side c must satisfy |a−b| < c < a+b.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.