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: a + b > c a + c > b b + c > a Question: 1. True or False: The segments of lengths 5, 7, and 10 can form a triangle.
True: The segments of lengths 5, 7, and 10 can form a triangle because they satisfy the triangle inequality theorem.
To check, we can apply the triangle inequality conditions:
1. 5 + 7 > 10 (12 > 10) - True
2. 5 + 10 > 7 (15 > 7) - True
3. 7 + 10 > 5 (17 > 5) - True
Since all the conditions are true, the segments of lengths 5, 7, and 10 can form a triangle.