Question

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

Answer 1

Euclid's fifth postulate is imply 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.

Answer 2

Answer:

Solution:

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.

So,

∠1+∠3=180

Or ∠3+∠4=180

____________________

Hope it will be helpful :)