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