"A polygon is convex if and only if a segment connecting any two vertices never passes through the exterior of the polygon."

If this statement is true, then which of the following statements must also be true?

A. A segment connecting any two vertices of a polygon never passes through the exterior of a polygon if and only if the polygon is not convex.
B. A polygon is not convex if and only if a segment connecting any two vertices never passes through the exterior of the polygon.
C. A polygon is convex if and only if a segment connecting any two vertices never passes through the interior of the polygon.
D. A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon.