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

Solution:

Euclid's fifth postulate: Given a line L and a point P not on the line, exactly one line can be drawn through P which is parallel to L.

Let's understand this.

For every line ‘l’ and for every point ‘P’ not lying on ‘l’, there exist a unique line ‘m’ passing through ‘P’ and parallel to ‘l’. This is called ‘Playfair’s Axiom’

• ‘l’ is a line and ‘p’ is a point not lying on ’l’.
• We can draw infinite lines through ‘p’ but there is only one line unique which is parallel to ‘l’ and passes through ‘p’.
• Take any point on ‘l’ and draw a line to ‘m’. Measure these distances.
• We know that it is the same everywhere, so these lines ‘l’ and ‘m’ do not meet anywhere.
• Hence, the two lines 'l' and 'm' are parallel.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 5

Video Solution:

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

NCERT Solutions Class 9 Maths Chapter 5 Exercise 5.2 Question 1

Summary:

Euclid’s fifth postulate can be written as "for every line ‘l’ and for every point ‘p’ not lying on ‘l', there exist a unique line ‘m′ passing through ‘p’ and parallel to ‘l', this is called ‘Playfair’s Axiom’

☛ Related Questions:

• In Fig. 5.10, if AC = BD, then prove that AB = CD.
• Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)
• Does Euclid fifth postulate imply the existence of parallel lines? Explain.