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# Answer to Question #299 in Geometry for Silvia Rosso

Question #299
Can a straight line, which intersects one of the parallel straight lines, do not intersect the other?
1
2010-06-15T08:36:38-0400
It&rsquo;s impossible if all three lines are in one plane. Let&rsquo;s call the parallel lines l and 2, the line, which intersects one of the parallel lines &ndash; 3. Let 3 intersects 1 in the point called A. If 3 doesn&rsquo;t intersect 2, 2 and 3 must be parallel. So we get that through the point A are drawn two lines, parallel to 2 &ndash; 1 and 3. According to the ninth Euclid&#039;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. But if 3 does not belong to the same plane as 1 and 2 belong, it can intersect 1 but do not intersect 2.

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