Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

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

Front

If two sides of a triangle are 5 and 7, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 2 and less than 12.

Front

Can a triangle have sides of lengths 2, 5, and 9?

Back

No, because 2 + 5 is not greater than 9.

Front

What is a possible third side to a triangle with side lengths of 13 and 4?

Back

12 is a possible length for the third side.

Front

Which set of numbers may represent the lengths of the sides of a triangle? {2,5,9}, {6,6,7}, {6,4,2}, {7,8,1}

Back

{6,6,7} can represent the lengths of the sides of a triangle.

Front

Which of the following would NOT work to make a triangle with the two side lengths of 2 and 6? 6, 7, 5, 4

Back

4 would not work because 2 + 6 is not greater than 4.

Front

Which of these lengths CANNOT represent the sides of a triangle? 32, 34, 60, 28, 30, 58, 13, 20, 27, 2, 4, 5

Back

28, 30, and 58 cannot represent the sides of a triangle.

Front

Given two sides of a triangle measuring 7 mm and 4 mm, what is the range for the third side?

Back

The third side must be more than 3 mm but less than 11 mm.

Front

What is the minimum length of the third side if the other two sides are 8 and 10?

Back

The minimum length of the third side must be greater than 2.

Front

If one side of a triangle is 15 and the other is 10, what is the maximum length of the third side?

Back

The maximum length of the third side can be 24.