The statement that verifies the Triangle Inequality Theorem is: "The sum of any two sides of a triangle is greater than the length of the third side."
This is the essence of the Triangle Inequality Theorem, which states that for any triangle with sides of lengths \( a \), \( b \), and \( c \), the following inequalities must hold:
- \( a + b > c \)
- \( a + c > b \)
- \( b + c > a \)