Definition of Parallel Lines

Parallel lines are straight lines that are always the same distance apart and never intersect, no matter how far they are extended in either direction

. They are coplanar, meaning they lie in the same plane

. The symbol used to denote parallel lines is ∥; for example, AB ∥ CD means line AB is parallel to line CD

Key Properties

• Always equidistant: The distance between parallel lines remains constant at every point

• Never intersect: Parallel lines do not meet or cross each other, even if extended infinitely

• Same direction: Parallel lines run in the same direction, which in coordinate geometry means they have the same slope

• Coplanar: They exist within the same plane

Identifying Parallel Lines

When a transversal (a line that crosses two or more other lines) intersects two parallel lines, several angle relationships arise:

• Corresponding angles are equal

• Alternate interior angles are equal

• Alternate exterior angles are equal

• Consecutive (same-side) interior angles are supplementary (add up to 180°)

Real-World Examples

• The opposite sides of a rectangle
• Railroad tracks
• Lines on ruled paper
• Roadway lane markings

Visual Representation

Parallel lines are often shown as two straight lines side by side with arrowheads indicating they continue infinitely in both directions

. In summary, parallel lines are straight, coplanar lines that never meet and always remain the same distance apart, forming a foundational concept in geometry