Triangle Inequality Theorem

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.

The following inequalities must hold: a + b > c, a + c > b, and b + c > a.

No, because 65 mm is not less than the sum of 32 mm and 33 mm (65 >= 32 + 33).

These measures do not form a triangle because 5 + 5 is not greater than 11.

Yes, these lengths form a triangle because 45 + 40 > 75, 45 + 75 > 40, and 40 + 75 > 45.

The sum of the lengths of any two sides must be greater than the length of the third side.

Yes, because 7 + 9 > 5, 7 + 5 > 9, and 9 + 5 > 7.

Yes, because 4 + 6 > 9, 4 + 9 > 6, and 6 + 9 > 4.

If one of the triangle inequalities is not satisfied, the three lengths cannot form a triangle.

The longest side must be less than the sum of the other two sides.