Fundamental Concepts
10. Parallel Lines · Lines that never meet
Lines AB and CD are parallel.
Two lines in a plane are parallel when they never meet, no matter how far they extend. Parallel lines have the same slope and are always the same distance apart. Drag C up or down — CD stays parallel to AB.
What this lesson covers
Try to break it
Drag point C. Watch what happens! The lines are no longer parallel. They are heading towards each other and would meet if produced.
How you build it
Draw two parallel lines.
- Place point A.
- Place point B to the right of A.
- Draw line AB.
- Place point C below A, at the same horizontal distance.
- Place point D below B, the same distance below as C is from A.
- Draw line CD. AB and CD never meet — parallel.
The proof, step by step
Prove that lines AB and CD are parallel.
- Lines AB and CD are both drawn in the same flat plane.
- No matter how far we extend them, AB and CD never meet.
- The perpendicular distance between AB and CD stays the same everywhere.
- Therefore, AB and CD are parallel lines.
Worked example
Two lines are said to be parallel if they:
Parallel lines are defined as lines in the same plane that do not intersect, no matter how far they are extended.
- Intersect at a right angle
- Never meet, even when produced to any extent — correct
- Meet at one point
- Are curved lines