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

Back

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

Front

Which of the following does not represent the lengths of the sides of a triangle: 2 cm, 6 cm, 7 cm, 5 cm, 2 cm, 5 cm, 5 cm, 5 cm, 8 cm, 3 cm, 10 cm, 15 cm?

Back

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

Front

What is the range of values for x if the other two sides of a triangle are 4 and 12?

Back

x must be between 8 and 16.

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

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

Back

Side lengths 1, 2, and 3 cannot form a triangle because 1 + 2 is not greater than 3.

Front

What is the minimum length of the third side if the other two sides are 5 and 7?

Back

The minimum length of the third side must be greater than 2 (5 - 7).

Front

What is the maximum length of the third side if the other two sides are 5 and 7?

Back

The maximum length of the third side must be less than 12 (5 + 7).

Front

If two sides of a triangle are 8 and 10, what is the range of possible lengths for the third side?

Back

The third side must be between 2 and 18.

Front

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

Back

The segments will be collinear and will not form a triangle.