Triangle Inequality

Step 1: Apply the triangle inequality theorem.
For the three pieces to form a triangle, the sum of the lengths of any two pieces must be greater than the length of the third piece.
Step 2: Analyze the options.
(A) is a necessary condition. If were greater than or equal to 0.5, the other pieces would be too small to form a triangle.
(B) is necessary because, if , the sum of the two smaller pieces would not be enough to form a triangle.
(C) is a necessary condition for forming a triangle, as it ensures the triangle inequality holds.
(D) is NOT a necessary condition for forming a triangle. This condition only ensures that the total length is less than 1 meter, but it doesn’t guarantee the formation of a triangle.