Prove that $\Box ABCD$ is a convex set whenever $\Box ABCD$ is a convex quadrilateral.
Things I know:
A set of points $S$ is said to be a convex set if for every pair of points $A$ and $B$ in $S$, the entire segment $AB$ is contained in $S$.
The diagonals of the quadrilateral $\Box ABCD$ are the segments $AC$ and $BD$
The angles of the quadrilateral $\Box ABCD$ are the angles $\angle ABC, \angle BCD, \angle CDA,$ and $\angle DAB$
A quadrilateral is said to be convex if each vertex of the quadrilateral is contained in the interior of the angle formed by the other three vertices.
How would I start this proof? Assuming that the quadrilateral $\Box ABCD$ is a convex quadrilateral.