Consider two 'postulates' given below:
(i) Given any two distinct points $ \mathrm{A} $ and $ \mathrm{B} $, there exists a third point $ \mathrm{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.

To do:

We have to consider the given postulates.

Solution:

Yes, these postulates contain undefined terms.

The position of $C$ is not defined. Whether the point lies on the line segment which joins $AB$ or not.

Whether all the points mentioned in postulates lie in the same plane or not.

Yes, these postulates are consistent as there are two different situations for the same undefined term (point $c$).

No, they do not follow from Euclid's postulates.

They follow one of the axioms.

That is,

Given any two points, a unique line passes through them.

Updated on: 10-Oct-2022

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