Answer to Question #300 in Geometry for kimb

Question

Can the line, which doesn’t contain any of triangle’s vertices, intersect all sides of this triangle? Why?

Answer 1

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.