Question

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

Answer 1

Answer:

Yes, Euclid's fifth postulate is valid for parallelism of lines because, if a straight line l falls on two straight 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 the line will not meet on this side of l.

Next, you know that the sum of the interior angles on the other side of line l will also be two right angles.

Therefore, they will not meet on the other side also. So, the lines m and n never meet and are, therefore, parallel.

Step-by-step explanation:

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