Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.
A. 8, 1, 7
B. 2, 7, 6
C. 9, 4, 3
D. 12, 10, 22
To apply the Triangle Inequality Theorem, we need to check if the sum of any two side lengths of a triangle must be greater than the third side length.
Let's check each group of side measures:
A. 8, 1, 7
The sum of the two shorter sides is 1 + 7 = 8, which is greater than the longest side of length 8. Therefore, this group of side measures (8, 1, 7) will form a triangle.
B. 2, 7, 6
The sum of the two shorter sides is 2 + 6 = 8, which is equal to the longest side of length 7. According to the Triangle Inequality Theorem, for a triangle to be formed, the sum of the lengths of any two sides must be strictly greater than the length of the remaining side. Since 8 is equal to 7, this group of side measures (2, 7, 6) will not form a triangle.
C. 9, 4, 3
The sum of the two shorter sides is 3 + 4 = 7, which is greater than the longest side of length 9. Therefore, this group of side measures (9, 4, 3) will form a triangle.
D. 12, 10, 22
The sum of the two shorter sides is 10 + 12 = 22, which is equal to the longest side of length 22. According to the Triangle Inequality Theorem, for a triangle to be formed, the sum of the lengths of any two sides must be strictly greater than the length of the remaining side. Since 22 is equal to 22, this group of side measures (12, 10, 22) will not form a triangle.
In summary, the triangles that will be formed are:
A. (8, 1, 7)
C. (9, 4, 3)