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

If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

Which of the following sets of lengths can form a triangle: 2, 3, 6?

Back

No, because 2 + 3 is not greater than 6.

Front

Can the lengths 5 cm, 5 cm, and 8 cm form a triangle?

Back

Yes, because 5 + 5 > 8, 5 + 8 > 5, and 5 + 8 > 5.

Front

What is the minimum length of the third side if two sides of a triangle are 7 cm and 10 cm?

Back

The minimum length of the third side must be greater than 3 cm (10 - 7).

Front

What is the maximum length of the third side if two sides of a triangle are 7 cm and 10 cm?

Back

The maximum length of the third side must be less than 17 cm (7 + 10).

Front

Which of the following cannot represent the sides of a triangle: 4, 5, 10?

Back

No, because 4 + 5 is not greater than 10.

Front

If a triangle has sides of lengths 6 cm, 8 cm, and x cm, what is the range of possible values for x?

Back

x must be greater than 2 cm and less than 14 cm.

Front

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

Back

5 cm, 7 cm, and 9 cm.

Front

What is an example of a set of lengths that cannot form a triangle?

Back

1 cm, 2 cm, and 3 cm.