Which statement can verify the Triangle Inequality Theorem?

Question

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

Answer 1

The statement that verifies the Triangle Inequality Theorem is:

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

The Triangle Inequality Theorem 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. \( b + c > a \)

Option A refers to the Pythagorean theorem, option C refers to the sum of angles in a triangle, and option D refers to properties of exterior angles, none of which are statements verifying the Triangle Inequality Theorem.