Triangle Inequality Theorem

🔑 Key Concepts

  • The sum of any two side lengths must be greater than the third side.
  • If one pair adds to less than the third side, the lengths cannot form a triangle.
  • If one pair adds to exactly the third side, the lengths form a straight line, not a triangle.
  • You can test all three combinations: \(a+b>c\), \(a+c>b\), and \(b+c>a\).

💡 Main Idea

The Triangle Inequality Theorem tells us whether three side lengths can make a triangle. For a triangle to exist, the sum of any two sides must always be greater than the third side. If even one sum is less than or equal to the third side, the side lengths do not form a triangle.

✏️ Worked Examples

🧠 Math Vocabulary

  • Triangle Inequality Theorem: The sum of any two side lengths of a triangle must be greater than the third side.
  • Side length: The distance from one vertex of a figure to another along an edge.
  • Greater than: A comparison showing that one quantity is larger than another.
  • Straight line: What happens when two side lengths add up exactly to the third instead of making a closed triangle.
  • Triangle construction: Determining whether given lengths can be connected to make a triangle.

📚 What You Should Already Know

Students should already know how to add whole numbers and compare values using symbols such as \(>\), \(<\), and \(=\).

🚀 What Comes Next

After learning the Triangle Inequality Theorem, students can apply this idea to triangle construction, missing side length problems, and reasoning about whether a set of measurements can create a valid triangle.

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