GL_LINE_SMOOTH works whereas GL_POLYGON_SMOOTH does not

Question

Here is my code:

#include <windows.h>
#include "GL/GL.h"
#include "GL/GLU.h"
#include "GL/glut.h"

void render()
{
    glClear(GL_COLOR_BUFFER_BIT);

    glBegin(GL_LINES);
    glColor3d(1, 0, 0);
    glVertex2d(0, -1);    
    glColor3d(0, 1, 0);
    glVertex2d(1, 1);
    glEnd();

    glBegin(GL_POLYGON);
    glColor3d(1, 0, 0);
    glVertex2d(-0.6, 0.3);
    glColor3d(0, 1, 0);
    glVertex2d(1, 1);
    glColor3d(0, 0, 1);
    glVertex2d(0, 0);
    glEnd();

    glFlush();
}

int main(int argc, char** argv)
{
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGBA);
    glutInitWindowSize(600, 400);
    glutInitWindowPosition(100, 100);
    glutCreateWindow("Lesson 1");
    glutDisplayFunc(render);

    glClearColor(0, 0, 0, 0);

    glEnable(GL_BLEND);
    glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);


    glEnable(GL_POINT_SMOOTH);
    glEnable(GL_LINE_SMOOTH);
    glEnable(GL_POLYGON_SMOOTH);

    glPointSize(10);
    glLineWidth(50);

    glutMainLoop();


    return 0;
}

And here is the result.

Why polygons are not anti-aliased? Please note that I have tried to use glHint(GL_POLYGON_SMOOTH_HINT, GL_NICEST); and it didn't help.