Answer to Question #301 in Geometry for TimS

Question

Two straight lines, which intersect, are given. Can a third line, which is parallel to each of given lines, be drawn?

Answer 1

No, it can’t. Let the given lines intersect in the point called A. If there is a third line, which is parallel to each of given lines, we can say that there are two lines, which are parallel to the third line and are drown through the point A. According to the ninth Euclid's axiom through the point, which does not lie on the line can be drawn no more than one parallel to it line. So, we get the contravention.