Prove by Induction for Minimum Triangle Count in a General Position of $n$ Lines in a Plane

Question

Suppose we have ≥3 lines in general position in the plane. How to prove by induction that these lines form at least −2 triangles?

Here, the general position means that no two lines are parallel, and no three lines intersect.

I can imagine that if we add one line to a collection of lines in general position, one triangle will be added because it will close the area between two lines in the outer surface. But I do not know whether my explanation is true, and make sense, or not.

Answer 1

Using the two definitions of general position you gave, you get that any 3 lines form a triangle. There are ${n}\choose{3}$ $\ge n-2$ such sets of 3 lines.