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

Yes, according to Euclid’s fifth postulate when line x falls on straight line y and z such that sum of the interior angles on one side of line x is two right angles.

$$\therefore$$ $$\angle{1}$$ + $$\angle{2}$$ = $$180^\circ$$.

Then, line y and line z on producing further will meet in the side of $$\angle{1}$$ and $$\angle{2}$$ which is less than $$180^\circ$$.

We find that the lines which are not according to Euclid’s fifth postulate.
$$\therefore$$ $$\angle{1}$$ + $$\angle{2}$$ = $$180^\circ$$, do not intersect.

So, the lines y and z never meet and are, therefore, parallel.