I want to prove that every normal planar graph has a straight-line embedding.
First, I assume that the planar graph $G$ is maximal planar, i.e the number of edges is $3n-6$ for $|G|=|V(G)|\ge3$. If the graph is not maximal planar I simply add some edges until it is maximal. I also know that all faces form triangles.
Now I want to prove the result with induction with respect to $n$.
$n=3:$ This case is trivial, it is just a triangle.
$n-1\rightarrow n$. I assume I know that the embedding works for a graph with $n-1$ vertices. I do not know hot to conclude. Intuitively it is clear to me because it is nothing more than some triangles which I clue together.
Maybe you can help me.