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? Explain.

3. 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? Explain.

Solutions :-

There are several undefined terms in the given postulates.

The given postulates are consistent because they refer to two different situations.

In first postulate two points A and B are given points then there will point C lying in the line between them 

Postulate (ii) states that for the given points A and B we can take point C not lying on the lines 

These postulates do not follow from Euclid’s postulates.  However they follow from the axiom, given two distinct points, there is a unique line that passes through them”.