Apply the triangle and quality theorem and determine which option could be the third side of a triangle if the first two sides measure four and six would it be nine or one or 11 or two?
Using the triangle inequality theorem, the third side of a triangle must be less than the sum of the other two sides.
In this case, the first two sides measure 4 and 6.
4 + 6 = 10
Therefore, the third side must be less than 10.
Out of the given options, 9 and 11 are greater than 10, so they cannot be the third side of the triangle.
Now, considering option 1 and 2:
For option 1: 4 + 1 = 5 which is less than 6, so option 1 could be the third side of the triangle.
For option 2: 4 + 2 = 6 which is equal to the second side, so option 2 could be the third side of the triangle.
Therefore, either 1 or 2 could be the third side of the triangle.