AFOQT Practice Test

According to the Triangle Inequality Theorem, what must be true about the lengths of the sides of a triangle?

1. The sum of the lengths of any two sides is less than the length of the third side

2. The difference between the lengths of any two sides is greater than the length of the third side

3. The sum of the lengths of any two sides is equal to the length of the third side

4. The sum of the lengths of any two sides is greater than the length of the third side

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

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This means that if you take any two sides of a triangle, when you add their lengths together, that sum will always exceed the length of the remaining side. This principle is crucial in geometry as it ensures that the three lengths can form a closed shape, which is necessary for the figure to be a triangle. The theorem helps distinguish valid triangle dimensions from invalid ones. If the sum of two sides were not greater than the third, the sides would not meet to form a triangle, which could lead to a straight line or a non-existent figure. This understanding reinforces the foundational aspects of triangle geometry and is a critical concept in both theoretical and practical applications.