Fundamental Concepts
11. When Lines Cross · Discovering the single point where two lines meet
Two non-parallel lines in a plane always meet at exactly one point.
Two non-parallel lines in a plane meet at exactly one point — their point of intersection. The crossing creates four angles in two pairs of equal vertically-opposite angles: same colour = same measure.
What this lesson covers
Try to break it
What if we move A and C so the lines look parallel? Remember, since they both pass through O, they can't be parallel!
How you build it
Draw two intersecting lines.
- Place point A.
- Place point B in a different direction.
- Draw line AB (Line tool: A then B).
- Place point C off the line AB.
- Place point D so that CD will cross AB.
- Draw line CD. Two non-parallel lines meet at one point.
The proof, step by step
Prove that the two lines intersect at exactly one point.
- Two lines lie in the same plane.
- The lines are not parallel.
- They meet at exactly one point O.
Worked example
Two lines in a plane are said to be intersecting lines if they:
Intersecting lines are defined as two lines in the same plane that are not parallel and meet at exactly one point.
- never meet
- meet at exactly one point — correct
- meet at two points
- are parallel