Chapter 5 – Introduction To Euclid’s Geometry Exercise 5.2

Que. 1 How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?

Ans

When two straight lines cuts by third straight line , such that the sum of interior angles is less than 1800 . And if both the straight line produced indefinately then they meet only in that side on which the sum of interior angles is less than 1800 .

Example:-

Suppose line C falls on  lines A and B , such that  the sum of interior angles is less than 1800

When line A and B produced indefinately, they meet only in that side  on which the sum of interior angles is less than 1800 .

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

Ans

Yes , Euclid’s fifth postulate imply the existence of parallel lines .Because :-

(i) If a line intersect two straight line, such that the sum of interior angles is less than 1800 then the lines eventually intersect .

(ii)If a line intersect two straight line, such that the sum of interior angles is 1800 , then the lines doesn’t  intersect .It means both the lines are parallel. And parallel lines never intersect each-other.

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