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Bot GPT 3.5 To apply the 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.
A. 8, 1, 7
The sum of 8 and 1 is 9, which is greater than 7. The sum of 1 and 7 is 8, which is greater than 8. The sum of 8 and 7 is 15, which is greater than 1. Therefore, this group of side measures (8, 1, 7) will form a triangle.
B. 12, 10, 22
The sum of 12 and 10 is 22, which is equal to the third side, 22. According to the Triangle Inequality Theorem, the sum of two sides should be greater than the third side, not equal to it. Therefore, this group of side measures (12, 10, 22) will not form a triangle.
C. 2, 7, 6
The sum of 2 and 7 is 9, which is greater than 6. The sum of 7 and 6 is 13, which is greater than 2. The sum of 2 and 6 is 8, which is greater than 7. Therefore, this group of side measures (2, 7, 6) will form a triangle.
D. 9, 4, 3
The sum of 9 and 4 is 13, which is greater than 3. The sum of 4 and 3 is 7, which is less than 9. The sum of 9 and 3 is 12, which is greater than 4. Therefore, this group of side measures (9, 4, 3) will not form a triangle.
In summary, the groups of side measures that will form a triangle are A. 8, 1, 7 and C. 2, 7, 6.