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

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.

∠1+∠3 = 180o

Or  ∠3+∠4 = 180o

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