Which statement is always true about the Triangle Inequality Theorem?

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 third side. This principle is fundamental in geometry and helps to establish whether a given set of lengths can actually form a triangle.

When evaluating any three lengths, if they can adhere to this theorem, then those lengths can indeed create a triangle. This means that if you take any two sides, their combined lengths must exceed the length of the remaining side. This characteristic ensures that, geometrically, the triangle can 'close' and not collapse into a straight line or fail to connect at all.

Thus, this statement is always true for any triangle and is essential for recognizing valid triangle configurations. The other options do not universally apply to all triangles: the perimeter being equal to the sum of the sides is a different statement regarding the total distance around the triangle and does not reflect the relationships between individual sides; one side being equal to the sum of the other two describes a degenerate triangle (which does not conform to the properties of traditional triangles); and stating that all sides are equal in length specifically refers to equilateral triangles, which is a subset of all triangles.