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

Which of the following sets of lengths can form a triangle? 2 cm, 2 cm, 5 cm; 3 cm, 4 cm, 5 cm; 1 cm, 1 cm, 3 cm.

Back

Only 3 cm, 4 cm, 5 cm can form a triangle.

Front

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

Back

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

Front

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

Back

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

Front

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

Back

The third side must be greater than 2 cm and less than 18 cm.

Front

Given sides of lengths 6 cm and 9 cm, what is the range of values for the third side?

Back

The third side must be greater than 3 cm and less than 15 cm.

Front

If the longest side of a triangle is 12 cm, what must be true about the other two sides?

Back

The sum of the lengths of the other two sides must be greater than 12 cm.

Front

What is the relationship between the sides of a triangle with lengths 5 cm, 5 cm, and 8 cm?

Back

These lengths satisfy the Triangle Inequality Theorem and can form an isosceles triangle.

Front

Can a triangle have sides of lengths 1 cm, 2 cm, and 3 cm?

Back

No, because 1 + 2 is not greater than 3.