1. How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?
. For every line l
and for every point P not on l
, there is a unique line n through P, which is parallel to l
. There can be other statements also.
2. Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.
Sol. 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 the lines, if produced indefinitely, will not meet on this side of l. In the same way, 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.