Consider two 'postulates' given below: (i) Given any two distinct points A and B, there exists a third point C which is in between A and B. (ii) There exist at least three points that are not on the same line. Do these postulates contain any undefined terms?

There are several undefined terms which we should keep in mind. They are consistent, because they deal with two different situations: (i) says that 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 can 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.