Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
8, 1, 7 8, 1, 7 2, 7, 6
9, 4, 3 9, 4, 3 12, 10, 22
To determine which group of side measures will form a triangle, we need to apply the Triangle Inequality Theorem.
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.
Let's check each set of side measures:
1. 8, 1, 7:
- 8 + 1 = 9, which is greater than 7
- 8 + 7 = 15, which is greater than 1
- 1 + 7 = 8, which is greater than 8
All the sums are greater than the third side, so this set of side measures forms a triangle.
2. 2, 7, 6:
- 2 + 7 = 9, which is greater than 6
- 2 + 6 = 8, which is less than 7
- 7 + 6 = 13, which is greater than 2
Not all sums are greater than the third side, so this set of side measures does not form a triangle.
3. 9, 4, 3:
- 9 + 4 = 13, which is greater than 3
- 9 + 3 = 12, which is greater than 4
- 4 + 3 = 7, which is less than 9
Not all sums are greater than the third side, so this set of side measures does not form a triangle.
4. 12, 10, 22:
- 12 + 10 = 22, which is equal to 22
- 12 + 22 = 34, which is greater than 10
- 10 + 22 = 32, which is greater than 12
All the sums are greater than the third side, so this set of side measures forms a triangle.
Therefore, the group of side measures that will form a triangle according to the Triangle Inequality Theorem is 8, 1, 7 and 12, 10, 22.