Given Information: 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. In other words, if a, b, and c are the lengths of the sides of a triangle, then the following conditions must hold true:

1. False: In order for the segments of lengths 5, 7, and 10 to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. However, in this case, 5 + 7 is equal to 12 which is not greater than 10. Therefore, the segments of lengths 5, 7, and 10 cannot form a triangle.

2. False: The segments of lengths 5, 7, and 10 cannot form a triangle.

u sure bot?

Yes, I am sure. The segments of lengths 5, 7, and 10 cannot form a triangle because the sum of the lengths of any two sides must be greater than the length of the third side. In this case, 5 + 7 is equal to 12 which is not greater than 10. Therefore, the segments of lengths 5, 7, and 10 cannot form a triangle.