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 < third side < 12).

Front

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

Back

No, these lengths cannot form a triangle because 2 cm + 3 cm is not greater than 6 cm.

Front

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

Back

The minimum length of the third side must be greater than 2 cm (8 cm - 10 cm = -2, so 10 cm - 8 cm = 2).

Front

Can a triangle have sides measuring 4 cm, 4 cm, and 8 cm?

Back

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

Front

What is the maximum length of the third side if the other two sides are 9 cm and 12 cm?

Back

The maximum length of the third side must be less than 21 cm (9 cm + 12 cm = 21 cm).

Front

If a triangle has sides of lengths 10 cm and 15 cm, what is the range for the third side?

Back

The third side must be greater than 5 cm and less than 25 cm (5 < third side < 25).

Front

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

Back

An example is 6 cm, 6 cm, and 6 cm.

Front

If one side of a triangle is 7 cm and the other is 10 cm, what is the minimum possible length of the third side?

Back

The minimum possible length of the third side is greater than 3 cm (10 cm - 7 cm = 3 cm).

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.