Final answer:
The statement that is always true is that two lines that remain the same distance apart are parallel. This geometric principle ensures that such lines never intersect, as opposed to perpendicular lines which intersect at 90 degrees.
Step-by-step explanation:
The question asks us to determine which statement about lines is always true. The correct statement is: Two lines that are always the same distance apart are parallel.
Here's why: Lines that share a common endpoint can be at any angle to each other; they're not necessarily perpendicular. Furthermore, lines that are always the same distance apart do not intersect and are always parallel, regardless of where they are positioned in a plane. This is because parallel lines never converge or diverge from each other as they extend. In contrast, two lines that are perpendicular intersect at a 90-degree angle, but this has nothing to do with the distance between them elsewhere.
The statement regarding distance apart is a fundamental principle used in geometry and plays a critical role in the concept of linear perspective in art, where parallel lines appear to converge at a distance, though they are, in fact, parallel.