To determine if the given side measures will form a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's analyze each set of side measures:
1) 2, 2, 1:
The sum of the two smaller sides is 2 + 1 = 3, which is not greater than the length of the remaining side (2).
Therefore, the measures 2, 2, 1 will not form a triangle.
2) 3, 3, 6:
The sum of the two smaller sides is 3 + 3 = 6, which is equal to the length of the remaining side (6).
Therefore, the measures 3, 3, 6 will not form a triangle.
3) 3, 3, 4:
The sum of the two smaller sides is 3 + 3 = 6, which is greater than the length of the remaining side (4).
Therefore, the measures 3, 3, 4 will form a triangle.
4) 2, 2, 2:
The sum of the two smaller sides is 2 + 2 = 4, which is equal to the length of the remaining side (2).
Therefore, the measures 2, 2, 2 will form a triangle.
So, the side measures that will not form a triangle are:
- 2, 2, 1
- 3, 3, 6