🔑 Key Concepts
- The Triangle Inequality Theorem determines whether three lengths can form a triangle.
- The sum of any two side lengths must be greater than the third side.
- You must check all three combinations of side lengths.
- If even one pair does not satisfy the rule, a triangle cannot be formed.
- If the sum equals the third side, the result is a straight line, not a triangle.
🧠 Math Vocabulary
- Triangle Inequality Theorem: A rule stating that 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 triangle to another.
- Valid Triangle: A set of lengths that satisfies all three triangle inequalities.
- Degenerate Triangle: A situation where the sum of two sides equals the third side, forming a straight line instead of a triangle.
- Inequality: A mathematical statement comparing values using symbols such as \( > \), \( < \), \( \ge \), or \( \le \).
💡 Main Idea
Three lengths can form a triangle only if the sum of any two sides is greater than the third side. If one pair is too short or exactly equal to the third side, the figure will not close to form a triangle. Always check all three combinations to be sure.
📚 What You Should Already Know
Students should understand how to add numbers, compare values using greater-than and less-than symbols, and recognize basic properties of triangles and line segments.
🚀 What Comes Next
Next, students will apply the Triangle Inequality Theorem to find possible side lengths, determine ranges of values for missing sides, and use triangle inequalities in geometric problem solving and construction tasks.
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