Lesson 7: Building Polygons Part 2
Triangle Inequality Exploration
Triangle Inequality Exploration
Triangle #1
Name three lengths that create a triangle
Triangle #2
Name three other lengths that create a triangle
Triangle #3
Name three other lengths that create a triangle
Triangle #4
Name three lengths that do not create a triangle
Triangle #5
Name three other lengths that do not create a triangle
Write down any observations you notice about the lengths that did make a triangle and did not make a triangle.
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, if you have three line segments with lengths a, b, and c, you can form a triangle if and only if the sum of any two of these lengths is greater than the length of the third.
For example
If you have line segments of length 3, 4, and 5, you can form a triangle because:
- 3 + 4 > 5
- 3 + 5 > 4
- 4 + 5 > 3
Prove It!
Based on the Triangle Inequality Theorem prove that one of your triangles is really a triangle
Prove It!
Based on the Triangle Inequality Theorem prove that one of your triangles is really NOT a triangle
Check for Understanding
Which of the following lengths creates a triangle? Select all that apply
Check for Understanding
Which of the following lengths does not create a triangle? Select all that apply