Answer to Question #300 in Geometry for kimb

Question #300
Can the line, which doesn’t contain any of triangle’s vertices, intersect all sides of this triangle? Why?
1
Expert's answer
2010-06-15T08:40:44-0400
Yes, it can. If there is such line and it intersects all sides of the triangle, each two vertices are placed in different half-planes. The triangle has three vertices, so there are must be at least three half-planes. But according to the fourth Euclid's axiom a line divides the plane into two half-plane only. So, we get the contravention.

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