Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

Given two sides of lengths 13 and 4, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than the difference of the two sides (13 - 4 = 9) and less than the sum of the two sides (13 + 4 = 17). Therefore, the possible lengths for the third side are between 9 and 17.

Front

Can the side lengths 2 inches, 2 inches, and 4 inches form a triangle?

Back

No, because 2 + 2 is not greater than 4, violating the Triangle Inequality Theorem.

Front

What is the condition for three lengths to form a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

If one side of a triangle is 9 and the other two sides are 28 and 30, can these lengths form a triangle?

Back

No, because 9 + 28 is not greater than 30.

Front

What is an example of side lengths that can form a triangle?

Back

Side lengths of 5, 7, and 10 can form a triangle because 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5.

Front

What is the maximum length of a side in a triangle with sides 10 and 15?

Back

The maximum length of the third side must be less than 10 + 15 = 25.

Front

What is the minimum length of a side in a triangle with sides 10 and 15?

Back

The minimum length of the third side must be greater than |10 - 15| = 5.

Front

If the sides of a triangle are 28, 30, and 58, do they form a triangle?

Back

No, because 28 + 30 is not greater than 58.

Front

What is the significance of the Triangle Inequality Theorem in geometry?

Back

It helps determine whether three given lengths can form a triangle, which is fundamental in triangle construction and analysis.