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

Can the side lengths 3, 5, and 8 form a triangle?

Back

No, because 3 + 5 is not greater than 8.

Front

Which of the following 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

Can the side lengths 7 yd, 8 yd, and 9 yd form a triangle?

Back

Yes, because 7 + 8 > 9, 7 + 9 > 8, and 8 + 9 > 7.

Front

Does a triangle with side lengths 15, 12, and 9 exist?

Back

Yes, because 15 + 12 > 9, 15 + 9 > 12, and 12 + 9 > 15.

Front

Given two sides of a triangle measuring 7 ft and 13 ft, what is the range for the length of the third side?

Back

The length of the third side must be more than 6 ft but less than 20 ft.

Front

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

Back

The maximum length of the third side is 24 cm (10 + 15 - 1).

Front

If the sides of a triangle are 5, 12, and 13, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 5 + 12 > 13, 5 + 13 > 12, and 12 + 13 > 5.

Front

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

Back

The minimum length of the third side must be more than 2 (10 - 8).

Front

Can a triangle have sides measuring 1, 2, and 3?

Back

No, because 1 + 2 is not greater than 3.