Split surface on line

[Philippe Hurbain]

I'm sure there's a simple way to do this but I don't know how in LDPE:
How do I split the quads and triangles along the bottom green line?

Not so simple... Since the green line seems parallel to main axis, you could possibly use symsplitter with "cut across the plane". But resulting triangulation is not so good...
What I would do would be to create intersection vertices between the edge lines around blue surfaces and green line (slanted x icon in toolbar) and rebuild things from there.