Question
Which statement can verify the Triangle Inequality Theorem?(1 point)
Responses
The three angles of a triangle will always amount to 180 degrees.
The three angles of a triangle will always amount to 180 degrees.
The sum of any two sides of a triangle is greater than the length of the third side.
The sum of any two sides of a triangle is greater than the length of the third side.
The formula a2+b2=c2 will find the length of the third side of any triangle.
The formula a squared plus b squared equals c squared will find the length of the third side of any triangle.
An exterior angle is equal to its two remote interior angles.
Responses
The three angles of a triangle will always amount to 180 degrees.
The three angles of a triangle will always amount to 180 degrees.
The sum of any two sides of a triangle is greater than the length of the third side.
The sum of any two sides of a triangle is greater than the length of the third side.
The formula a2+b2=c2 will find the length of the third side of any triangle.
The formula a squared plus b squared equals c squared will find the length of the third side of any triangle.
An exterior angle is equal to its two remote interior angles.
Answers
GPT-4o mini
The statement that can verify the Triangle Inequality Theorem is:
**The sum of any two sides of a triangle is greater than the length of the third side.**
This statement directly expresses the Triangle Inequality Theorem, which states that for any triangle with sides of lengths \( a \), \( b \), and \( c \), the following inequalities must hold:
1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)
**The sum of any two sides of a triangle is greater than the length of the third side.**
This statement directly expresses the Triangle Inequality Theorem, which states that for any triangle with sides of lengths \( a \), \( b \), and \( c \), the following inequalities must hold:
1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)