To determine if a set of side measures will form a triangle, we need to apply the Triangle Inequality Theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For each set of side measures:
1) 9 + 4 = 13, which is greater than 3. Furthermore, 9 + 3 = 12, which is greater than 4. Lastly, 4 + 3 = 7, which is less than 9. Therefore, the measures 9, 4, and 3 will not form a triangle.
2) 8 + 1 = 9, which is greater than 7. Furthermore, 8 + 7 = 15, which is greater than 1. Lastly, 1 + 7 = 8, which is less than 8. Therefore, the measures 8, 1, and 7 will form a triangle.
3) 2 + 7 = 9, which is greater than 6. Furthermore, 2 + 6 = 8, which is less than 7. Lastly, 7 + 6 = 13, which is greater than 2. Therefore, the measures 2, 7, and 6 will form a triangle.
4) 12 + 10 = 22, which is equal to 22. Furthermore, 12 + 22 = 34, which is greater than 10. Lastly, 10 + 22 = 32, which is greater than 12. Therefore, the measures 12, 10, and 22 will form a triangle.
In conclusion, the group of side measures that will form a triangle is 8, 1, and 7.
Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
9, 4, 3
8, 1, 7
2, 7, 6
12, 10, 22
1 answer