The sum of any two sides of a triangle is:

The correct answer is: greater than the third side.

To understand why this is correct, we can look at the Triangle Inequality Theorem, a fundamental principle in geometry.
This theorem states that for any valid triangle, the sum of the lengths of any two sides must always be strictly greater than the length of the remaining third side.

Let us represent the lengths of the three sides of a triangle as $a$, $b$, and $c$.
For these three lengths to form a non-degenerate triangle, the following three conditions must simultaneously hold true:

$a+b>c$

$a+c>b$

$b+c>a$

If the sum of any two sides were equal to the third side (e.g., $a+b=c$), the three vertices would lie on a single straight line, resulting in a flat, degenerate segment rather than a triangle.
If the sum were less than the third side (e.g., $a+b<c$), the two shorter sides would not be long enough to connect with each other, making it impossible to close the shape and form a triangle.

Therefore, the sum of any two sides of a triangle is always greater than the third side.