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Question -

Does Euclid’s fifth postulate imply the existence of parallel lines ? Explain.



Answer -

Yes. If a straight line l falls on two lines m and n such that sum of the interior angles on one side of l is two right angles, then by Euclid’s fifth postulate, lines m and n will not meet on this side of l. Also, we know that the sum of the interior angles on the other side of the line l will be two right angles too. Thus, they will not meet on the other side also.
∴ The lines m and n never meet, i.e, They are parallel.

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