Problem

Source: Iran 3rd round 2011-final exam-p3

Tags: geometry proposed, geometry



We have connected four metal pieces to each other such that they have formed a tetragon in space and also the angle between two connected metal pieces can vary. In the case that the tetragon can't be put in the plane, we've marked a point on each of the pieces such that they are all on a plane. Prove that as the tetragon varies, that four points remain on a plane. proposed by Erfan Salavati