Introduction to Euclid Geometry (Exercise 5.2)

Introduction to Euclid Geometry


Chapter 5


Exercise 5.2


EX 5.2 QUESTION 1.


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

If two lines intersect the third line in such a way that the sum of the interior angles is less than 180°, then the two lines intersect each other.


EX 5.2 QUESTION 2.


Does Euclid’s fifth postulate imply the existence of parallel lines ? Explain.
Solution:

Yes, Euclid’s fifth postulate does imply the existence of the parallel lines. Because if two lines intersect the third line in such a way that the sum of the interior angles is less than 180°, then the two lines intersect each other but if the sum of interior angles is 180°, then the lines don’t intersect or line are parallel.