Apply the triangle inequality theorem and determine which group of side measures will form a triangle answer choices. 12,10,22. Or 9,4,3 or 8,1,7 or 2,7,6

Answer 1

To determine which 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.

Let's apply this theorem to the given side measures:

1. 12, 10, 22:
12 + 10 = 22, which is greater than 22. However, the sum of the other pairs is not greater than the third side, so these side measures will not form a triangle.

2. 9, 4, 3:
9 + 4 = 13, which is greater than 3. Additionally, 9 + 3 = 12 and 4 + 3 = 7 are both greater than the remaining side. Therefore, these side measures will form a triangle.

3. 8, 1, 7:
8 + 1 = 9, which is greater than 7. Additionally, 8 + 7 = 15 and 1 + 7 = 8 are both greater than the remaining side. Therefore, these side measures will form a triangle.

4. 2, 7, 6:
2 + 7 = 9, which is greater than 6. Additionally, 2 + 6 = 8 and 7 + 6 = 13 are both greater than the remaining side. Therefore, these side measures will form a triangle.

So, the groups of side measures that will form a triangle are 9, 4, 3 and 2, 7, 6.