Question

does Euclid fifth postulate imply the existence of parallel lines?​

Answer 1

Answer:

If a straight line l falls on the two straight lines m & n such that the sum of the interior angles on one side of l is two right angles , then by Euclid's fifth postulate the lines will not meet on the sides of l .

We know that the sum of the interior angles on the other side of line and will also be two right angles . Hence, they will not meet on the other side also. So the lines m & n never meet and are therefore parallel.

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Hope this will help you......

Answer 2

Yes, Euclid’s fifth postulate does imply the existence of the parallel lines.

If the sum of the interior angles is equal to the sum of the right angles, then the two lines will not meet each other at any given point, hence making them parallel to each other.

∠1+∠3 = 180°

Or ∠3+∠4 = 180°