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 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.
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.
Apply the Triangle Inequality Theorem to determine whether sides with lengths of 5 inches, 10 inches, and 15 inches form a triangle.(1 point)
Responses
Yes, because the sum of 5+10 is not greater than 15.
Yes, because the sum of 5 plus 10 is not greater than 15.
Yes, because the sum of 5+10 is less than or equal to 15.
Yes, because the sum of 5 plus 10 is less than or equal to 15.
Yes, the majority of the conditions are met.
Yes, the majority of the conditions are met.
No, because the sum of 5+10 is not greater than
Yes, because the sum of 5+10 is less than or equal to 15.
Apply the Triangle Inequality Theorem to determine whether sides with lengths of 3 inches, 4 inches, and 9 inches form a triangle.(1 point)
Responses
Yes, because 3+4 is less than 9.
Yes, because 3 plus 4 is less than 9.
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.
Yes, the majority of the conditions are met.
Yes, the majority of the conditions are met.
No, because 3+4 is less than 9.
No, because 3+4 is less than 9.
To determine if a triangle can be formed from sides of lengths 7 millimeters, 8 millimeters, and 9 millimeters, we need to apply the Triangle Inequality Theorem.
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.
Let's check if this holds true for our given sides:
7 + 8 = 15 (which is greater than 9)
7 + 9 = 16 (which is greater than 8)
8 + 9 = 17 (which is greater than 7)
Since the sum of each pair of sides is greater than the third side in all cases, we can conclude that a triangle can be formed from sides of lengths 7 millimeters, 8 millimeters, and 9 millimeters.
Therefore, the correct response is:
Yes, because the sum of any two sides is greater than the third side.