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Which statement BEST describes the triangle inequality theorem?The sum of any two side lengths in a triangle must be exactly 180∘.The sum of any two side lengths in a triangle must be greater than the length of the third side.The sum of any two side lengths in a triangle must be greater than 180∘.The sum of any one side length in a triangle must be greater than the difference of the second and third side.

Question

Which statement BEST describes the triangle inequality theorem?The sum of any two side lengths in a triangle must be exactly 180∘.The sum of any two side lengths in a triangle must be greater than the length of the third side.The sum of any two side lengths in a triangle must be greater than 180∘.The sum of any one side length in a triangle must be greater than the difference of the second and third side.

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Solution

Sure, let's analyze each statement step by step to determine which one best describes the triangle inequality theorem.

  1. The sum of any two side lengths in a triangle must be exactly 180∘.

    • This statement is incorrect. The sum of the angles in a triangle is 180 degrees, not the side lengths.
  2. The sum of any two side lengths in a triangle must be greater than the length of the third side.

    • This statement is correct. The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
  3. The sum of any two side lengths in a triangle must be greater than 180∘.

    • This statement is incorrect. The sum of the side lengths is not related to 180 degrees.
  4. The sum of any one side length in a triangle must be greater than the difference of the second and third side.

    • This statement is partially correct but not a complete description of the triangle inequality theorem. It is true that the length of any side must be greater than the difference of the other two sides, but the theorem is more commonly stated as the sum of any two sides being greater than the third side.

Therefore, the statement that best describes the triangle inequality theorem is:

The sum of any two side lengths in a triangle must be greater than the length of the third side.

This problem has been solved

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