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 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 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 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 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.
To apply the Triangle Inequality Theorem, you need to compare the sum of any two sides of the triangle with the length of the third side.
In this case, the given lengths are 7 millimeters, 8 millimeters, and 9 millimeters. Let's check if the sum of any two sides is greater than the third side:
1. Sum of 7 millimeters and 8 millimeters = 15 millimeters. Is it greater than 9 millimeters? Yes.
2. Sum of 7 millimeters and 9 millimeters = 16 millimeters. Is it greater than 8 millimeters? Yes.
3. Sum of 8 millimeters and 9 millimeters = 17 millimeters. Is it greater than 7 millimeters? Yes.
Since the sum of any two sides is greater than the third side for all the combinations, it satisfies the Triangle Inequality Theorem. Therefore, YES, a triangle can be formed from sides with lengths 7 millimeters, 8 millimeters, and 9 millimeters.