Introduction to Euclid's Geometry : Exercise 5.2 (Mathematics NCERT Class 9th)

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Q.1     How would you rewrite Euclid's fifth postulate so that it would be easier to understand?
Sol.       The axiom asserts two facts :
(i) There is a line through P which is parallel to l and
              (ii) There is only one such line.

Q.2      Does Euclid's Fifth postulate imply the existence of parallel lines? Explain.

If a straight line l falls on two straight lines m and n such that the sum of the interior angles on one side of l is two right angles, then by Euclid's fifth postulate the lines will not meet on this side of l. Next, we 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.


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