There are several undefined terms which we should keep in mind. They are consistent, because they deal with two different situations:(i) says that the given two points A and B, there is a point C lying on the line in between them;(ii) says that given A and B, we ca take C not lying on the line through A and B.These ‘postulates’ do not follow from Euclid’s postulates. However, they follow from axiom stated as given two distinct points; there is a unique line that passes through them.