A polygon is called convex if every interior angle is less than \(180^\circ\), i.e: the shape doesn’t “bulge inwards". Show that if a quadrilateral \(ABCD\) has a convex quadrilateral \(EFGH\) situated completely inside it, then the perimeter of \(ABCD\) is greater than the perimeter of \(EFGH\). You might want to remind yourself of the triangle inequality: in any triangle \(DEF\), the side \(DE\) is always shorter than going around the other two sides, so \(DE < DF + FE\).