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)
• 11
• 2
• 9
• 1
To apply 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.
If the first two sides of the triangle measure 4 and 6, then using the Triangle Inequality Theorem, the third side must be less than the sum of these two sides (4 + 6 = 10).
Out of the given options, 11 is greater than 10 and cannot be the third side of the triangle.
Similarly, 9 is also greater than 10 and cannot be the third side of the triangle.
Option 2 (2) is less than 10 and can be the third side of the triangle.
Option 1 (11) and option 3 (9) do not satisfy the Triangle Inequality Theorem.
Therefore, the third side of the triangle could be 2.