To apply the Triangle Inequality Theorem, we need to check if the sum of the lengths of two sides of a triangle is greater than the length of the third side.
Let's check each group of side measures:
1) 9, 4, 3
The sum of the lengths of the two smaller sides is 4 + 3 = 7, which is greater than the length of the longest side, 9.
Therefore, the group of side measures 9, 4, 3 will form a triangle.
2) 9, 4, 31
The sum of the lengths of the two smaller sides is 4 + 31 = 35, which is greater than the length of the longest side, 9.
Therefore, the group of side measures 9, 4, 31 will form a triangle.
3) 2, 10, 22
The sum of the lengths of the two smaller sides is 2 + 10 = 12, which is less than the length of the longest side, 22.
Therefore, the group of side measures 2, 10, 22 will not form a triangle.
4) 12, 10, 22
The sum of the lengths of the two smaller sides is 12 + 10 = 22, which is equal to the length of the longest side, 22.
Therefore, the group of side measures 12, 10, 22 will form a degenerate triangle, which is a triangle with collinear vertices.
5) 8, 1, 7
The sum of the lengths of the two smaller sides is 1 + 7 = 8, which is equal to the length of the longest side, 8.
Therefore, the group of side measures 8, 1, 7 will form a degenerate triangle.
6) 2, 7, 6
The sum of the lengths of the two smaller sides is 2 + 6 = 8, which is greater than the length of the longest side, 7.
Therefore, the group of side measures 2, 7, 6 will form a triangle.
In conclusion, the groups of side measures that will form a triangle are:
- 9, 4, 3
- 9, 4, 31
- 2, 7, 6
Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)Responses9, 4, 39, 4, 312, 10, 2212, 10, 228, 1, 78, 1, 72, 7, 6
1 answer
1 answer