Apply the Triangle Inequality Theorem to determine whether sides with lengths of 4 inches, 8 inches, and 9 inches form a triangle.(1 point)
Responses
No, all of the conditions are not met.
No, all of the conditions are not met.
Yes, the majority of the conditions are met.
Yes, the majority of the conditions are met.
Yes, all of the conditions are met.
Yes, all of the conditions are met.
No, because two out of three conditions are met
No, all of the conditions are not met.
To apply the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides of the triangle is greater than the length of the remaining side.
Let's check:
1. The sum of 4 inches and 8 inches is 12 inches, which is less than 9 inches. (4 + 8 < 9).
2. The sum of 4 inches and 9 inches is 13 inches, which is less than 8 inches. (4 + 9 < 8).
3. The sum of 8 inches and 9 inches is 17 inches, which is greater than 4 inches. (8 + 9 > 4).
Since two out of the three conditions are not met, we can conclude that the sides with lengths of 4 inches, 8 inches, and 9 inches do not form a triangle.
Therefore, the correct response is:
No, all of the conditions are not met.
To apply the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides of the triangle is greater than the length of the third side. Let's check:
1. Sum of the lengths of the first two sides: 4 inches + 8 inches = 12 inches. Is 12 inches greater than the length of the third side (9 inches)? Yes.
2. Sum of the lengths of the first and third sides: 4 inches + 9 inches = 13 inches. Is 13 inches greater than the length of the second side (8 inches)? Yes.
3. Sum of the lengths of the second and third sides: 8 inches + 9 inches = 17 inches. Is 17 inches greater than the length of the first side (4 inches)? Yes.
Since the sum of the lengths of any two sides is greater than the length of the third side, 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.
The correct response is: Yes, all of the conditions are met.