Apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle if the first two sides measure 4 and 6.(1 point)
Responses
9
9
2
2
1
1
11
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, the first two sides measure 4 and 6. Testing the options:
1) 9 - The sum of 4 and 6 is 10, which is greater than 9. Therefore, option 9 could be the third side of a triangle.
2) 2 - The sum of 4 and 6 is 10, which is greater than 2. Therefore, option 2 could be the third side of a triangle.
3) 1 - The sum of 4 and 6 is 10, which is greater than 1. Therefore, option 1 could be the third side of a triangle.
4) 11 - The sum of 4 and 6 is 10, which is not greater than 11. Therefore, option 11 could not be the third side of a triangle.
In summary, options 9, 2, and 1 could be the third side of a triangle, but option 11 could not.