Final answer:
The side lengths of 9ft, 1ft, and 6ft do not satisfy the Triangle Inequality Theorem; thus, no triangle can be formed with these lengths.
Step-by-step explanation:
The question asks whether the given side lengths of 9ft, 1ft, and 6ft would determine a unique triangle, similar triangles, nonidentical triangles, or no triangle at all. To determine this, we can use the Triangle Inequality Theorem. In any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
In this case, adding the two shortest sides, 1ft and 6ft, gives us 7ft, which is not greater than the length of the longest side, 9ft. Therefore, these lengths do not satisfy the Triangle Inequality Theorem, meaning that no triangle can be formed with these three side lengths.
In order for the given conditions to determine a unique triangle, the length of one side of the triangle must be greater than the difference of the lengths of the other two sides, and less than the sum of the lengths of the other two sides. However, in this case, the given lengths of 9 ft, 1 ft, and 6 ft do not satisfy this inequality.
Therefore, the given conditions do not determine a unique triangle.