Question

Which statement can verify the Triangle Inequality Theorem?(1 point) Responses The three angles of a triangle will always amount to 180 degrees. The three angles of a triangle will always amount to 180 degrees. The formula a2+b2=c2 will find the length of the third side of any triangle. The formula a squared plus b squared equals c squared will find the length of the third side of any triangle. An exterior angle is equal to its two remote interior angles. An exterior angle is equal to its two remote interior angles. The sum of any two sides of a triangle is greater than the length of the third side.

Answer 1

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:

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)