AFOQT Practice Test

What does the Triangle Inequality Theorem state?

1. The sum of the angles in a triangle is always 180 degrees

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

3. The difference between the lengths of any two sides of a triangle is less than the length of the third side

4. Both A and B are correct

The correct answer is: The sum of the lengths of any two sides of a triangle is greater than the length of the third side

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is essential in geometry because it establishes a fundamental property regarding the relationship of the sides in any triangle. This rule ensures that three given lengths can form a triangle. While the other statements concerning the properties of triangles are true, they pertain to different aspects of triangle geometry. For instance, the sum of the angles in a triangle being always 180 degrees is a separate principle known as the Angle Sum Theorem, which, while accurate, does not relate to the side lengths in question here. The option mentioning the difference between the lengths of two sides emphasizes a different concept, which is not the primary focus of the Triangle Inequality Theorem. Thus, the answer provided aligns perfectly with the core content of the theorem regarding side lengths.