Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point) Responses 9, 4, 3 9, 4, 3 2, 7, 6 2, 7, 6 8, 1, 7 8, 1, 7 12, 10, 22
To determine if a set of side measures will form a triangle, we need to apply 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.
For the given side measures:
1) 9, 4, 3
The sum of the lengths of any two sides is as follows:
9 + 4 = 13
9 + 3 = 12
4 + 3 = 7
Since the longest side measure (9) is greater than the sum of the other two side measures (4 and 3), this set of side measures will form a triangle.
2) 2, 7, 6
The sum of the lengths of any two sides is as follows:
2 + 7 = 9
2 + 6 = 8
7 + 6 = 13
Since the longest side measure (7) is not greater than the sum of the other two side measures (2 and 6), this set of side measures will not form a triangle.
3) 8, 1, 7
The sum of the lengths of any two sides is as follows:
8 + 1 = 9
8 + 7 = 15
1 + 7 = 8
Since the longest side measure (8) is not greater than the sum of the other two side measures (1 and 7), this set of side measures will not form a triangle.
4) 12, 10, 22
The sum of the lengths of any two sides is as follows:
12 + 10 = 22
12 + 22 = 34
10 + 22 = 32
Since the longest side measure (22) is not greater than the sum of the other two side measures (12 and 10), this set of side measures will not form a triangle.
Therefore, the only group of side measures that will form a triangle is 9, 4, 3.