Apply the I riangle 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)

Question

1
2
11
9

Answer 1

To determine if a third side can form a triangle with sides measuring 4 and 6, we use 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 test each option:

1) 4 + 1 > 6
This is true, so 1 could be the third side of a triangle.

2) 4 + 2 > 6
This is true, so 2 could be the third side of a triangle.

3) 4 + 11 > 6
This is false, as 15 is not greater than 6. Therefore, 11 could not be the third side of a triangle.

4) 4 + 9 > 6
This is true, so 9 could be the third side of a triangle.

Therefore, options 1, 2, and 9 could be the third side of a triangle with sides measuring 4 and 6.