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

Back

The length of the third side must be greater than 2 cm and less than 12 cm (2 < x < 12).

Front

Which of the following sets of lengths can form a triangle: 3 cm, 4 cm, 8 cm?

Back

No, these lengths cannot form a triangle because 3 + 4 is not greater than 8.

Front

What is the minimum length of the third side if the other two sides are 10 cm and 15 cm?

Back

The minimum length of the third side must be greater than 5 cm.

Front

If one side of a triangle is 6 ft and another is 10 ft, what is the maximum length of the third side?

Back

The maximum length of the third side can be less than 16 ft.

Front

Given sides of lengths 8 mm and 12 mm, what is the range for the third side?

Back

The third side must be greater than 4 mm and less than 20 mm (4 < x < 20).

Front

Can the lengths 2 cm, 2 cm, and 5 cm form a triangle?

Back

No, these lengths cannot form a triangle because 2 + 2 is not greater than 5.

Front

What is the range of values for x if the sides of a triangle are 9 and 14?

Back

The range for x is 5 < x < 23.

Front

If two sides of a triangle are 7 m and 3 m, what is the minimum length of the third side?

Back

The minimum length of the third side must be greater than 4 m.

Front

What does it mean if a set of lengths does not satisfy the Triangle Inequality Theorem?

Back

It means that the lengths cannot form a triangle.