ok if you want a corner then the best thing to do is
either split between the top left vert and the bottom center and then split btween the center of the new edge to the top right and then snap the new corner into place or delete the face that is on the corner and select one of the edges attached to one of the verts and extrude it toward the other vert to create a new polygon and then merge the vertices.Then use the append to polgon tool to fill the gaps.
Another option is to use the append to polygon tool which will allow you to select the two edges of the gap and fill it but this will create a 3 sided polygon in your case so you would then have to add a vert by selecting the splitedge tool and placing a vert near the center of the diagonal face and then hitting enter and then snap it in the x direction only to be level with one of the original verts and then select the other (z) direction and snap it again to be level with the other.
To snap to a vert hold down V and middle mouse drag over the vert you want to snap to.
Finally you could then use the append to polygon tool to fill the two remaining holes.
I personally would extrude an edge then snap the two new verts of the new polygon to be level with the other vert,then merge the two vertices that are on top of each other.