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 180^{0} . 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 180^{0} .

Example:-

Suppose line C falls on lines A and B , such that the sum of interior angles is less than 180^{0}

When line A and B produced indefinately, they meet only in that side on which the sum of interior angles is less than 180^{0} .

## 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 180^{0} then the lines eventually intersect .

(ii)If a line intersect two straight line, such that the sum of interior angles is 180^{0} , then the lines doesn’t intersect .It means both the lines are parallel. And parallel lines never intersect each-other.