Question

consider the following statement there exists a pair of straight lines that are everywhere equidistant from one another. is this statement of direct consequence of euclid's fifth postulate? Explain​

Answer 1

True statement

Explanation:-

A pair of straight lines that are everywhere equidistant from one another.

For this:- Take any line l and a point P not on l. Then by play Fair's axiom, which is equivalent to the fifth postulate, we know that there is a unique line m through P which is parallel to l.

Now, the distance of a point from a line is the length of the perpendicular from the point to the line. This distance will be the same for any point on m from l and any point on l from m. Thus these two lines are everywhere equidistance from one another.