Apply the Triangle Inequality Theorem to determine whether a triangle can be formed from sides of lengths 7 millimeters, 8 millimeters, and 9 millimeters.(1 point)
Responses
No, because the sum of any two sides is greater than the third side.
No, because the sum of any two sides is greater than the third side.
Yes, because the sum of any two sides is less than the third side.
Yes, because the sum of any two sides is less than the third side.
No, because the sum of any two sides is less than the third side.
No, because the sum of any two sides is less than the third side.
Yes, because the sum of any two sides is greater than the third side.
No, because the sum of any two sides is greater than the third side.
No, because the sum of any two sides is greater than the third side.
The Triangle Inequality Theorem states that 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, we have three side lengths: 7 millimeters, 8 millimeters, and 9 millimeters.
To apply the Triangle Inequality Theorem, we need to check if the sum of any two sides is greater than the third side.
Let's start by checking 7 millimeters + 8 millimeters. The sum is 15 millimeters. Is 15 millimeters greater than 9 millimeters? Yes, it is. So the first condition is satisfied.
Next, let's check 7 millimeters + 9 millimeters. The sum is 16 millimeters. Is 16 millimeters greater than 8 millimeters? Yes, it is. So the second condition is satisfied.
Finally, let's check 8 millimeters + 9 millimeters. The sum is 17 millimeters. Is 17 millimeters greater than 7 millimeters? Yes, it is. So the third condition is satisfied.
Since all three conditions are satisfied, we can conclude that a triangle can be formed from sides of lengths 7 millimeters, 8 millimeters, and 9 millimeters.
Therefore, the correct answer is:
Yes, because the sum of any two sides is greater than the third side.