Triangle Inequality Theorem (Ordering and Forming Triangles)

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.

3, 6, 12 and 7, 7, 14 will NOT form a triangle because they do not satisfy the Triangle Inequality Theorem.

The length of the third side must be between 7 inches and 27 inches (10 + 17 > AC > 17 - 10). Thus, 16 inches is a valid length.

5, 9, 12.

The longest side of a triangle is opposite the largest angle.

In a triangle, the larger the angle, the longer the side opposite that angle.

It is an isosceles triangle.

The minimum length must be greater than 2 (10 - 8).

The maximum length must be less than 12 (5 + 7).

The smallest angle is opposite the shortest side, which is 5.