Question

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

Answer 1

Yes.

According to Euclid’s 5^th 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°.

If ∠1 + ∠2 = 180°, then ∠3 + ∠4 = 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.