Select the correct statement about the properties of a triangle.

To determine the correct statement about the properties of a triangle, we need to analyze the relationship between the lengths of its three sides. Let the lengths of the three sides of a triangle be represented by the variables a, b, and c.

For any valid non-degenerate triangle, a fundamental geometric principle known as the Triangle Inequality Theorem must be satisfied. This theorem states that the distance along a straight line between two points is always shorter than any path involving a third point not on that line.

Mathematically, the Triangle Inequality Theorem requires that the following three inequalities must simultaneously be true:
$a+b>c$
$a+c>b$
$b+c>a$
In simple terms, the sum of the lengths of any two sides of a triangle must always be strictly greater than the length of the remaining third side.

Let's evaluate the given options based on this theorem:
1. "The sum of two sides may be equal to the third side." - This is incorrect. If the sum of two sides is equal to the third side (e.g., $a+b=c$), the three vertices will lie on a single straight line, resulting in a collinear set of points rather than a triangle.
2. "The sum of two sides is always equal to the third side." - This is incorrect for the same reason of collinearity.
3. "The sum of two sides is always greater than the third side." - This matches the Triangle Inequality Theorem and is the correct property.
4. "The sum of two sides is always less than the third side." - This is physically impossible because the shortest path between two vertices is a straight line; a detour through a third vertex cannot be shorter.

Therefore, the correct statement is: The sum of two sides is always greater than the third side.