Proof: Theorem 7.2
Theorem 7.2
Theorem 7.2: Each point in an affine plane of order lies on lines.
Proof: Let be an arbitrary line. By Theorem 7.1, we know that has k points. Let p be an arbitrary point not on . By Axiom 2, every point on must have exactly one line in common with p. By Axiom 3, p has exactly one line parallel to .
Therefore, any point in an affine plane of order has lines.