A polygon is called convex if every interior angle is less than \(180^\circ\), that is, the shape does not “bulge inwards”. In a convex quadrilateral \(ABCD\), all the triangles \(\triangle ABC\), \(\triangle BCD\), \(\triangle CDA\) and \(\triangle DAB\) have equal perimeters. Show that \(ABCD\) is a rectangle.