To determine which set of side measures will NOT form a triangle, we can apply the triangle inequality theorem. According to this theorem, for any three lengths \(a\), \(b\), and \(c\), the sum of the lengths of any two sides must be greater than the length of the third side.
Let’s evaluate each set:
-
2, 2, 1:
- \(2 + 2 > 1\) (True)
- \(2 + 1 > 2\) (True)
- \(2 + 1 > 2\) (True)
- This set forms a triangle.
-
3, 3, 6:
- \(3 + 3 > 6\) (False)
- \(3 + 6 > 3\) (True)
- \(3 + 6 > 3\) (True)
- This set does NOT form a triangle.
-
3, 3, 4:
- \(3 + 3 > 4\) (True)
- \(3 + 4 > 3\) (True)
- \(3 + 4 > 3\) (True)
- This set forms a triangle.
-
2, 2, 2:
- \(2 + 2 > 2\) (True)
- \(2 + 2 > 2\) (True)
- \(2 + 2 > 2\) (True)
- This set forms a triangle.
Based on this analysis, the side measures that will NOT form a triangle are:
3, 3, 6
3 answers