Question

"Question 3 Consider the two ‘postulates’ given below: (i) Given any two distinct points A and B, there exists a third point C, which is between A and B. (ii) There exists 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.

Class 9 - Math - Introduction to Euclid's Geometry Page 85"

Answer 1

Solution:

There are so many undefined terms which should be listed they are consistent because they deal with two different situations which are as follows:

1.
If two points A and B are given then there exist a third point C which is in between A and B.

2.
If two points A and B are given then we can take a point C which do not lie on the line passing through the points A and B . Thus these points do not contradict each other.

These postulates do not follow Euclid's postulates. However they follow axiom. Euclid postulate 1 axiom states that through two distinct points there is a unique lines that passes through them.

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Hope this will help you....

Answer 2

Hey there!

Does this postulate contain undefined terms?

Yes, Points & lines are the undefined terms. Here (i) talks about collinear terms where as (ii) talks about non - collinear points.

Are these postulates consistent?

Yes,These are consistent, as they speak about collinear points, non -collinear points.

Do they follow euclids postulates?

Yes, Euclid told that there exist a point which is dividing the line into two parts which is given as mid point here. Though they add up new things. They follow the euclidean axioms in geometry