(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.

Question

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? Are these postulates consistent? Do they follow from Euclid’s postulates? Explian.

Answer 1

There are many undefined terms for students. They are consistent, because they deal with two different situations. 

(i) When two points A and B ar given, C is in between two. 

(ii) When two points A and B are given take point C which passes through A and B. 

These postulates do not follow from Euclid’s postulates. But they follow Axiom 2.1