Consider the following claim: The vertices of a triangle ABC are not collinear.

1. Is it true or false for E²? H²? S²? P²? The cylinder? The cone?
2. Give a proof or a counter-example for each space. (You may use one proof for more than one space, if appropriate.) Hint: Try giving a proof by contradiction, i.e., assume that the vertices are collinear and derive a contradiction. Alternatively, prove the contrapositive, i.e. consider a trilateral so ABC with A, B, C are collinear, and prove that it is degenerate.