Euclid's fifth postulate was restated in another form to be known as ____ axiom.

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Detailed Solution

Euclid's fifth postulate was restated in another form to be known as Playfair’s axiom.
Given Euclid’s fifth postulate.
For every postulate there can be other equivalent versions in which that postulate can be expressed. Euclid's fifth postulate is also having several equivalent versions, 'Playfair's axiom' is one of them.
Euclid's fifth postulate was restated in another form that is known as "Playfair's Axiom". In geometry this axiom can be used in place of Euclid's fifth postulate. This is given by a Scottish mathematician John Playfair in 1729 which can be stated as "For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to l"
Question Image

In the figure above we can see that from all the lines that are passing through point P, there is only one line m is parallel to line I.
Thus, Euclid's fifth postulate was restated in another form to be known as Playfair's axiom.
Therefore, the correct answer is Playfair’s.

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