G 10
Exercises for the three-point geometry.
1. Does each pair of lines in the geometry intersect in a point?
2. Through a point not on a given line, is there at least one line not intersecting the given line?
3. For each of two distinct points, does there exist exactly one line on both of them?
4. Exactly how many points are on each line?
5. Through a point not on a given line, there are how many lines parallel to the given line? (Use the "normal" definition of parallel).
6. Could three lines all contain the same point?
7. Do any squares exist? (Use the "normal" definition of square).
8. Rewrite the axioms, definition(s), and theorems of the three-point geometry using the word student for point and the word committee for line.