please help with antialiasing blending !

In OpenGL help I saw that for polygon antialiasing we shuold use blending as
following:
glEnable(GL_POLYGON_SMOOTH);
glEnable(GL_BLENDING);
glBlendFunc (GL_SRC_ALPHA_SATURATE, GL_ONE);
Of course I set opacity of the polygons color to 1.0 ,but I got
empty window…
Than I try blending function for lines:
glBlendFunc (GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
This works,but I still see transparent lines
going through my polygons.(I guess these lines are antialising triangles that divides my polygons).How to fix it?Actually to make these lines in the color of polygons is the solution ,but how to do it?