Final answer:
Yes, it is possible to form a triangle with segments measuring 3, 5, and 7 inches because the sum of the lengths of any two sides is greater than the length of the third side, satisfying the triangle inequality theorem.
Step-by-step explanation:
The question was to determine whether it is possible to form a triangle using a set of segments with the measurements 3, 5, and 7. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we can check the following:
- 3 + 5 > 7: This is true because 8 is greater than 7.
- 3 + 7 > 5: This is true because 10 is greater than 5.
- 5 + 7 > 3: This is true because 12 is greater than 3.
Since all conditions are satisfied, we can conclude that it is indeed possible to form a triangle with these three segments.