1st incidence axiom (Does Not Hold)[br]For every line, l, and for every line, m, not intersecting l, there exists a unique plane P incident with l and m.[br][br]The model of Euclidean 3-space where lines replace points and planes [br]replace lines does not satisfy the first incidence axiom. Consider the [br]line through the points (0, 0, 0) and (1, 1, 1) and the line through the[br] points (-1, -1, 0) and (0, -1, 1). The lines represented by these [br]points are called skew lines and do not define a plane.[br][br]2nd incidence axiom (Holds)[br]For all planes, P, there is at least two distinct lines incident with P.[br][br]There are an infinite number of parallel lines that are distinct and incident with a given plane.[br][br]3rd incidence axiom (Holds)[br]There are 3 distinct non-coplanar lines.[br][br]Certainly 3 parallel lines could be arranged to be non-coplanar.