Apply the Triangle Inequality Theorem to determine whether sides with lengths of 4 inches, 8 inches, and 9 inches form a triangle.
No, because two out of three conditions are met.
Yes, all of the conditions are met.
Yes, the majority of the conditions are met.
No, all of the conditions are not met.
No, all of the conditions are not met.
Yes, all of the conditions are met.
According to 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.
In this case, the sum of the lengths of the sides with lengths of 4 inches and 8 inches is 12 inches, which is greater than the length of the third side (9 inches).
Similarly, the sum of the lengths of the sides with lengths of 4 inches and 9 inches is 13 inches, which is also greater than the length of the third side (8 inches).
Lastly, the sum of the lengths of the sides with lengths of 8 inches and 9 inches is 17 inches, which is greater than the length of the third side (4 inches).
Therefore, all of the conditions are met and these side lengths form a triangle.
To determine whether the sides with lengths of 4 inches, 8 inches, and 9 inches form a triangle, we can apply the Triangle Inequality Theorem. According to this theorem, for a triangle to be formed, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check if this holds true for the given side lengths:
1. Sum of 4 inches and 8 inches: 4 + 8 = 12 inches
Is it greater than 9 inches? Yes, it is.
2. Sum of 4 inches and 9 inches: 4 + 9 = 13 inches
Is it greater than 8 inches? Yes, it is.
3. Sum of 8 inches and 9 inches: 8 + 9 = 17 inches
Is it greater than 4 inches? Yes, it is.
Since the sum of the lengths of any two sides is greater than the length of the third side for the given side lengths, we can conclude that all of the conditions of the Triangle Inequality Theorem are met. Therefore, the sides with lengths of 4 inches, 8 inches, and 9 inches do form a triangle. Thus, the correct answer is "Yes, all of the conditions are met."