Connect edge with perpendicular edge Is there a way to connect the selected face (white in the image) to the edge in front of it?



Result should create two vertices in the facing edge and simply merge the selected edge with the newly created edge.

Hope I made myself clear.
The fastest solution in this case may be using a knife tool. Press K and snap the knife to the vertices. After pressing the LMB press C to make the cut go straight and cut the longer piece horizontally. Repeat the process for the other vertex. Now you can use a bridge tool to connect pieces (and then dissolve the unnecessary edge). You may also use a snapping tool (vertex) to connect pieces and then remove doubles.