I'm facing the following problem: I have a plane with a set of simple convex polygons on top of it. I'm required to prove that however I pick two vertices, one as a starting point and one as a target, the minimum distance between them will consist of straight line segments, each of which joining two vertices. The following image will illustrate the idea (shortest path from S to G in red).
I'm struggling to figure out how to start proving that this is the case. Please no complete proof since that's my task, I appreciate any hint to the right direction.
EDIT: Forgot to mention that the path can't cut a polygon, as in no point of the path can be inside any of them.