Apply the Triangle Inequality Theorem to determine whether sides with lengths of 4 inches, 8 inches, and 9 inches form a triangle. (1 point)
No, because two out of three conditions are met.
Yes, all of the conditions are met.
O No, all of the conditions are not met.
O Yes, the majority of the conditions are met.
No, because two out of three conditions are met.
To apply the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Let's test it out with the given side lengths of 4 inches, 8 inches, and 9 inches.
First, we'll try adding the lengths of the shortest sides (4 inches and 8 inches) and compare it to the length of the longest side (9 inches):
4 + 8 = 12 inches
Since 12 inches is greater than 9 inches, the first condition is met.
Next, we'll add the lengths of the remaining two sides (4 inches and 9 inches) and compare it to the length of the remaining side (8 inches):
4 + 9 = 13 inches
Again, 13 inches is greater than 8 inches, so the second condition is met.
Finally, we add the lengths of the remaining two sides (8 inches and 9 inches) and compare it to the length of the remaining side (4 inches):
8 + 9 = 17 inches
Once again, 17 inches is greater than 4 inches, so the third condition is met.
Since all three conditions are met, we can conclude that the given side lengths of 4 inches, 8 inches, and 9 inches do form a triangle.
Therefore, the correct answer is: Yes, all of the conditions are met.