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 simpler terms, if you have three lengths, $a$, $b$, and $c$, they can only form a triangle if the following three inequalities are all true: $a + b > c$, $a + c > b$, and $b + c > a$.
This theorem helps us determine whether a triangle can exist with given side lengths. If even one of these conditions isn't met, a triangle cannot be formed!
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. Triangle Inequality Theorem | A. A closed figure with three sides and three angles. |
| 2. Side | B. A line segment connecting two vertices in a polygon. |
| 3. Triangle | C. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. |
| 4. Sum | D. The result of adding two or more numbers. |
| 5. Inequality | E. A mathematical statement that compares two expressions using symbols like >, <, ≥, or ≤. |
Complete the following paragraph with the correct words:
The Triangle Inequality Theorem states that the ______ of any two sides of a ______ must be ______ than the length of the ______ side. If this condition is not met, a triangle ______ be formed.
Explain in your own words why the Triangle Inequality Theorem is important in geometry. Provide a real-world example where this theorem might be useful.
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