NCERT solution ,with extra information[Exercise 5.2]Lesson no.5 Introduction to Euclid's Geometry

5 . Introduction to Euclid's Geometry 

Equivalent Versions of Euclid's Fifth Postulates

There are several equivalent version of this postulate.

One of them is:

"For every line and every point P not  lyineg on L, There exist new line 'N' passing to P & parallel to L."

       OR

"Two distance intersecting lines cannot be parallel to the same line."

Ex .Digram :

Exercise 5.2 

Que.1] How would you reside euclid's fifth postulate so that it would be easier to understand?

Ans: Two lines and said to be parallel to each other if-

I) They do not intersect at any point 

ii) They are equal distance from each other.

iii) a = b {Distance between two parallel lines are equal.}

Que.2] Does euclid's fifth postulate imply the existence of parallel line? Explain.

Ans :  Yes, according to euclid's fifth postulate imply the existence of parallel lines.

{ From fig. 1 }

Angle 1 +Angle 2 <180°

Angle 3 +Angle 4 > 180°

Thus, the line will meet on producing. 

But if { from fig .2 }

Angle 1+ Angle 2= 180 °

Angle 3 +Angle 4 = 180°

So, the line will not meet on producing on either of sides.

Hence, it can be said to that parellel lines exist .