consider two 'postulates' given below :
(1). Give any two dinstict poiny A and B, there exists a third point tjat are not on the same line.
(2).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 fro. Euclid's postulated ? explain.
>please answer correctly .
(1). Give any two dinstict poiny A and B, there exists a third point tjat are not on the same line.
(2).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 fro. Euclid's postulated ? explain.
>please answer correctly .
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Answer:
There are several undefined terms which we should keep in mind. They are consistent, because they deal with two different situations:
(i) says that the given two points A and B, there is a point C lying on the line in between them;
(ii) says that given A and B, we ca take C not lying on the line through A and B.
These ‘postulates’ do not follow from Euclid’s postulates. However, they follow from axiom stated as given two distinct points; there is a unique line that passes through them.
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There are several undefined terms which we should keep in mind. They are consistent, because they deal with two different situations:
(i) says that the given two points A and B, there is a point C lying on the line in between them;
(ii) says that given A and B, we ca take C not lying on the line through A and B.
These ‘postulates’ do not follow from Euclid’s postulates. However, they follow from axiom stated as given two distinct points; there is a unique line that passes through them.