Question

Does Euclid' fifth postulate imply the existence of parallel lines? Explain

• A. True
• B. False

Answer 1

The correct option is A True

Yes, Euclid's fifth postulate is valid for parallelism of lines because, if a straight line $l$ falls on two straight lines $m$ and $n$ such that sum of the interior angles on one side of $l$ is two right angles, then by Euclid's fifth postulate the line will not meet on this side of $l$.

Next, you know that the sum of the interior angles on the other side of line $l$ will also be two right angles.

Therefore, they will not meet on the other side also. So, the lines $m$ and $n$ never meet and are, therefore, parallel.