Does Euclid fifth postulate imply the existence of parallel lines.Explain?
Euclid himself, probably, had mixed feelings about it as he did not make use of it until Proposition I.29. The postulate looks more like another proposition than a basic truth. Here’s, for example, Proposition I.27 which, combined with Proposition I.13, claims that, if internal angles sum up to two right angles, then the lines are parallel.) If a straight line crossing two straight lines makes the alternate angles equal to one another, the straight lines will be parallel to one another.
