Answer to Question #262 in Geometry for Roberta

Question

Straight lines a and b are given. These lines don’t belong to the same plane. Can we draw a straight line, which is parallel to each of these lines?

Answer 1

No, we can’t. It’s a well known fact, that two lines, which are parallel to the third line, are parallel to each other. So, if we can draw this line, we get that a and b are parallel. It means we can build a plane, which contains both these lines, so they belong to the same plane. So, we get the contravention.