Two lines intersect if and only if they share a point.
Two lines are parallel if and only if they do not intersect.
The four point geometry is defined by the following axioms and definitions.
- There exist exactly four points.
- Any two distinct points have exactly one line on both of them.
- Each line is on exactly two points.
Explore the four point geometry as follows.
- Draw and label four points.
- Use axiom 2 to draw as many lines as possible.
- How many lines exist in this geometry?
- Find a pair of parallel lines.
- Can you find three lines that are pairwise parallel?
- Can you find a point that is on three lines?