Does Euclid's fifth postulate imply the existence of parallel lines? Thumz up assured. PLz answer fast.
Yes, Euclid's fifth postulates imply the existence of parallel lines.
If a straight line l falls on two straight lines m and n, such that sum of interior angles on one side of l is two right angles, then according to Euclid's fifth postulate they do not meet on this side of l.
Since the sum of two interior angles on the other side of l is also right angle , then m and n do not intersect on the other side also.
Therefore, m and n do not intersect on either side, thus the lines are parallel.
Hope this helps you.
If a straight line l falls on two straight lines m and n, such that sum of interior angles on one side of l is two right angles, then according to Euclid's fifth postulate they do not meet on this side of l.
Since the sum of two interior angles on the other side of l is also right angle , then m and n do not intersect on the other side also.
Therefore, m and n do not intersect on either side, thus the lines are parallel.
Hope this helps you.