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 11 11 1 1 9 9 2
The Triangle Inequality Theorem states that 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 two given sides measure 4 and 6. Let's test each option to see if it could be the third side of a triangle:
1. 11: 4 + 6 > 11 → 10 > 11 (False)
2. 1: 4 + 6 > 1 → 10 > 1 (True)
3. 9: 4 + 6 > 9 → 10 > 9 (True)
4. 2: 4 + 6 > 2 → 10 > 2 (True)
Based on the Triangle Inequality Theorem, the options that could be the third side of a triangle are 1, 9, and 2.