Question

"Question 2 Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

Class 9 - Math - Introduction to Euclid's Geometry Page 88"

Answer 1

Solution:

If a straight line l falls on the two straight lines m & 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 the sides of l .

 We know that the sum of the interior angles on the other side of line and will also be two right angles . Hence, they will not meet on the other side also.  So the lines m & n never meet and are therefore parallel.

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Answer 2

Hi friend...
If a straight line L falls on the 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 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.||

Hope it is helpful...