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

What is the minimum length of the third side if two sides of a triangle are 7 ft and 13 ft?

Back

The minimum length of the third side must be greater than 6 ft.

Front

Can the side lengths 2 cm, 6 cm, and 7 cm form a triangle?

Back

Yes, because 2 + 6 > 7, 2 + 7 > 6, and 6 + 7 > 2.

Front

What is the maximum length of the third side if two sides of a triangle are 7 ft and 13 ft?

Back

The maximum length of the third side must be less than 20 ft.

Front

Which of the following sets of lengths cannot form a triangle: 2 cm, 6 cm, 7 cm or 3 cm, 10 cm, 15 cm?

Back

3 cm, 10 cm, 15 cm cannot form a triangle.

Front

If the longest side of a triangle is 10, what must be true about the other two sides?

Back

The sum of the lengths of the other two sides must be greater than 10.

Front

What is an example of side lengths that satisfy the Triangle Inequality Theorem?

Back

Side lengths of 5 cm, 7 cm, and 9 cm satisfy the theorem.

Front

What happens if the sum of two sides of a triangle equals the length of the third side?

Back

If the sum of two sides equals the length of the third side, the segments are collinear and do not form a triangle.

Front

If one side of a triangle is 8 cm and another is 5 cm, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 3 cm and less than 13 cm.