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The sum of any two sides of a triangle i...

The sum of any two sides of a triangle is always ...... than the third side.

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To solve the question, "The sum of any two sides of a triangle is always ...... than the third side," we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Triangle**: - Consider a triangle with vertices A, B, and C. The sides of the triangle are AB, AC, and BC. 2. **Identifying the Sides**: - Let’s denote the sides as follows: - Side 1: AB - Side 2: AC - Side 3: BC 3. **Applying the Triangle Inequality Theorem**: - According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. - This can be expressed in three inequalities: - AB + AC > BC - AB + BC > AC - AC + BC > AB 4. **Conclusion**: - From the inequalities, we can conclude that the sum of any two sides of a triangle is always greater than the third side. 5. **Final Answer**: - Therefore, the answer to the question is: "The sum of any two sides of a triangle is always **greater** than the third side."
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