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.

The length of the third side must be greater than 2 (7 - 5) and less than 12 (5 + 7), so the range is (2, 12).

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

No, because 3 + 4 is not greater than 8.

The smallest angle is opposite the shortest side, which is 6.

The maximum possible length of the third side is 23 (10 + 14 - 1).

The minimum possible length of the third side is 4 (14 - 10 + 1).

Use the Triangle Inequality Theorem: check if the sum of any two lengths is greater than the third length.

The longest side is opposite the 90° angle.