apply the triangle inequality theorem and which group of side measures will form a triangle
1. 12, 10, 22
2. 9, 4, 3
3. 8, 1, 7
4. 2, 7, 6
1. In 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.
For group of side measures (12, 10, 22):
12 + 10 = 22 (not greater than 22)
12 + 22 = 34 (greater than 10)
10 + 22 = 32 (greater than 12)
Therefore, the group of side measures (12, 10, 22) will form a triangle.
2. For group of side measures (9, 4, 3):
9 + 4 = 13 (greater than 3)
9 + 3 = 12 (greater than 4)
4 + 3 = 7 (greater than 9)
Therefore, the group of side measures (9, 4, 3) will form a triangle.
3. For group of side measures (8, 1, 7):
8 + 1 = 9 (greater than 7)
8 + 7 = 15 (greater than 1)
1 + 7 = 8 (not greater than 8)
Therefore, the group of side measures (8, 1, 7) will form a triangle.
4. For group of side measures (2, 7, 6):
2 + 7 = 9 (greater than 6)
2 + 6 = 8 (not greater than 7)
7 + 6 = 13 (greater than 2)
Therefore, the group of side measures (2, 7, 6) will form a triangle.