Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
2, 7, 6
8, 1, 7
12, 10, 22
9, 4, 3
To determine whether a set of side measures can form a triangle, we can apply the Triangle Inequality Theorem, which states that for any triangle, the sum of the lengths of two sides must be greater than the length of the third side.
Let's apply this theorem to each group of side measures:
1) 2, 7, 6
2 + 7 = 9 > 6
Since the sum of the two smaller sides (2 and 7) is greater than the largest side (6), this group of side measures (2, 7, 6) can form a triangle.
2) 8, 1, 7
8 + 1 = 9 > 7
Again, the sum of the two smaller sides (8 and 1) is greater than the largest side (7), so this group of side measures (8, 1, 7) can form a triangle.
3) 12, 10, 22
12 + 10 = 22 = 22
In this case, the sum of the two smaller sides (12 and 10) is equal to the largest side (22). According to the Triangle Inequality Theorem, the sum of the two smaller sides should be greater than the largest side for a triangle to be formed. Since it is not greater, this group of side measures (12, 10, 22) cannot form a triangle.
4) 9, 4, 3
4 + 3 = 7 > 9
Once again, the sum of the two smaller sides (4 and 3) is less than the largest side (9), so this group of side measures (9, 4, 3) cannot form a triangle.
Therefore, the groups of side measures (2, 7, 6) and (8, 1, 7) will form triangles.