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.