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# Is it true if a line is parallel to plane it is parallel to any line in the plane?

Updated: 11/3/2022

Wiki User

14y ago

If your definition of parallel lines is that they never meet, then the answer is yes. If, however, the definition is that they remain equidistant from one another at all points, then, in my opinion, the answer is no.

It is difficult to explain the second without recourse to diagrams which are very difficult to manage on this site. So consider a cube with vertices ABCD forming the top face and EFGH (in corresponding order) forming the bottom face.

Now AB is parallel to the bottom plane - EFGH. And AB is clearly parallel to EF and any line parallel to EF. But is AB parallel lines such as FG? True, they will never meet but the distance between them increases as you move away from BF - ie they are not the same distance apart.

Incidentally, Euclid's parallel postulate was phrased in a very different way from the one most mathematicians come across it. That version is a much later equivalent statement.

Wiki User

14y ago