which statement can verify the Triangle inequality theorem?

Question

A. The sum of any two sides of a triangle is greater than the length of the third side
B. an exterior angle is equal to its two remote interior angles
C. The three angles of a triangle will always amount to 180 degrees
D. The formula a^2 + b^2 = c^2 will find the length of the third side of any triangle

Answer 1

The statement that verifies the Triangle Inequality Theorem is:

A. The sum of any two sides of a triangle is greater than the length of the third side.

This is the definition of the Triangle Inequality Theorem, which states that for any triangle with sides of lengths \( a \), \( b \), and \( c \), the following conditions must hold:

• \( a + b > c \)
• \( a + c > b \)
• \( b + c > a \)