Which type of lines exist in the same plane but never intersect?

The correct answer is parallel lines, as they are defined by the unique property of being in the same plane but never intersecting, regardless of how far they are extended in either direction. Parallel lines maintain a constant distance from one another, which allows them to avoid crossing.

In contrast, perpendicular lines intersect at a right angle, which means they cannot be parallel. Secant lines, by definition, intersect a curve at two or more points, thus they also do not fit the criteria of never intersecting. Tangent lines touch a curve at exactly one point, indicating that they only meet at that single location and do not extend beyond that point in the same way parallel lines do. Therefore, parallel lines stand out as the only type that never meet or cross within the same plane.