Lines which are exactly the same distance apart at all points are said to be __________ to each other.

Lines that are exactly the same distance apart at all points are defined as parallel. This means that no matter how far you extend the lines in either direction, they will never meet or intersect; the distance between them remains constant. In a geometric context, parallel lines have the same slope and are typically described using a coordinate system where they maintain a uniform distance, which distinguishes them from other types of lines. This concept is foundational in both geometry and engineering, where understanding the relationships between lines is essential for design and analysis.

The other provided options do not fit this definition. Perpendicular lines intersect at a right angle, which is contradictory to the concept of maintaining equal distance. Tangential lines touch a curve at exactly one point but do not maintain distance as they proceed beyond that point. Equal, while suggesting the idea of sameness, does not pertain specifically to the relationship between the distance of lines in a geometric context. Therefore, the appropriate term for lines that maintain a consistent distance apart is indeed parallel.