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

Back

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

Front

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

Back

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

Front

What is the range of lengths for the third side of a triangle with sides 7 mm and 4 mm?

Back

3 < x < 11.

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 two shorter sides must be greater than 10.

Front

Select the measurements that can form a triangle: 7, 9, 19, 7, 12, 1, 7, 7, 7, 7, 7, 16.

Back

7, 7, 7 can form a triangle.

Front

What is the minimum length of the third side if two sides of a triangle are 4 and 7?

Back

The minimum length of the third side must be greater than 3.

Front

What is the maximum length of the third side if two sides of a triangle are 4 and 7?

Back

The maximum length of the third side must be less than 11.

Front

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

Back

3 < x < 13.

Front

What does it mean if the sum of two sides of a triangle equals the length of the third side?

Back

It means the three points are collinear and do not form a triangle.