Statement: Prove, under the assumption of the parallel postulate (P-1), parallelism of lines is transitive. That is if l||m and m||q, then l||q. Parallel Postulate(p-1)-If l is any line and point P not on l there exists an unique line passing through P parallel to l( in the plane of P,l). Proof- Assume to the contrary that l is not parallel to q. Further assume the parallel postulate p-1. Sine l is not parallel to q that means both lines meet at least 1 point.But that's a contradiction since it contradicts parallel postulate p-1. Is that correct? or do i need to explain it a bit more why it contradicts?
asked Feb 22, 2013 at 16:38
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$\begingroup$ You should explain why it's a contradiction. $\endgroup$
Commented Feb 22, 2013 at 16:42
$\begingroup$ I would explain more, maybe by taking $P$ to be the intersection of $l$ and $q$ and chasing down what the parallel postulate gives you. $\endgroup$
Commented Feb 22, 2013 at 16:44