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Question

Consider the following statement:

There exists a pair of straight lines that are everywhere equidistant from one another.
Is this statement a direct consequence of Euclid's fifth postulate? Explain

A
True
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B
False
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Solution

The correct option is A True
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.

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