Professor Halfbrain has recently made several fascinating discoveries on cutting convex polygons in the plane.
Halfbrain's second cutting theorem: Every convex polygon can be cut (by a perfectly straight cut) into two polygons $A$ and $B$ so that $A$ and $B$ have the same perimeter and so that the length of the shortest side of $A$ equals the length of the shortest side of $B$.
Question: Is this second theorem indeed true, or has the professor once again made one of his notorious mathematical blunders?
1. A convex polygon has $n$ pairwise distinct vertices. A side of the polygon is the straight line segment connecting two consecutive vertices along the convex hull.
2. For the professor's first cutting theorem, see Professor Halfbrain's first cutting theorem.