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.