Chapter 3 Introduction to Euclid’s Geometry Ex 3.2
How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?
Two distinct intersecting lines cannot be parallel to the same line.
Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.
According to Euclid’s fifth postulate when line x falls on line y and z such that ∠1+ ∠2< 180°. Then, line y and line z on producing further will meet in the side of ∠1 arid ∠2 which is less than 180°.
We find that the lines which are not according to Euclid’s fifth postulate. i.e., ∠1 + ∠2 = 180°, do not intersect.