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

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According to Euclid’s 5th postulate, when n line falls on l and m and if ∠1 + ∠2 < 180°, then ∠3 + ∠4 > 180°producing line l and m further will meet in the side of ∠1 and ∠2 which is less than 180°.

The lines l and m neither meet at the side of ∠1 and ∠2 nor at the side of ∠3 and ∠4. This means that the lines l and m will never intersect each other. Therefore, it can be said that the lines are parallel.

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