To determine if a group of side measures will form a triangle, we can 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.
1. For the side measures 9, 4, 3:
- 9 + 4 > 3 (True)
- 9 + 3 > 4 (True)
- 4 + 3 > 9 (False)
Therefore, the side measures 9, 4, 3 will NOT form a triangle.
2. For the side measures 12, 10, 22:
- 12 + 10 > 22 (False)
- 12 + 22 > 10 (True)
- 10 + 22 > 12 (True)
Therefore, the side measures 12, 10, 22 will NOT form a triangle.
3. For the side measures 8, 1, 7:
- 8 + 1 > 7 (True)
- 8 + 7 > 1 (True)
- 1 + 7 > 8 (True)
Therefore, the side measures 8, 1, 7 WILL form a triangle.
4. For the side measures 2, 7, 6:
- 2 + 7 > 6 (True)
- 2 + 6 > 7 (True)
- 7 + 6 > 2 (True)
Therefore, the side measures 2, 7, 6 WILL form a triangle.
Therefore, the groups of side measures that will form a triangle are 8, 1, 7 and 2, 7, 6.
Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
9, 4, 3
12, 10, 22
8, 1, 7
2, 7, 6
1 answer