Minkowski sums of Convex Hulls

Question

How do I prove that the Convexhull(p1) +(Minskowski Sum) Convexhull(p2) = Convexhull(p1+p2), Where p1 and p2 are convex polygons.

Answer 1

Since $p_1$ and $p_2$ are convex, you have $\text{CH}(p_1)=p_1$ and $\text{CH}(p_2)=p_2$.

Since $p_1$ and $p_2$ are convex, $p_1+p_2$ is also convex so $\text{CH}(p_1+p_2)=p_1+p_2$.