# Connecting points to form triangles

$$3n$$ points are drawn on a flat piece of paper, such that no $$3$$ points lie on a straight line. Is it always possible to connect triples of points with straight lines, such that you form $$n$$ triangles and no two triangles intersect or touch each other?

• Trivially no if all 3n points are on a line. Probably you mean that no three points are on a single line? Dec 8 '21 at 11:59
• @Bubbler yes i agree, having 9 points in a 3x3 grid , its not possible to connect pairs of points to form N triangles. Plus I fail to understand what the OP means by pairs points while referring to 3 sets of points. Dec 8 '21 at 12:07
• ah sorry, forgot about collinear points. Will update. Dec 8 '21 at 12:15