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 atleast 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.

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 atleast 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.

There are so many undefined words which should be knowledge.

They are consistent because they deal with two different situations i.e.,

(i) If two points A and B are given, then there exists a third point C which is lying in between A and B on the line.

(ii) If two points A and B are given, then we can take a point C which don’t lie on the line passing
through the point A and B.

These postulates do not follow Euclid’s postulate.

However, they follow axiom Euclid’s postulate 1
stated as "through two distinct points, there is a unique line that passes through them."