I know this is old and all. But there is a much easier way of doing it. Just Extrude one Vertex from one of the Vertex of the Edge you want, select the snap to Edge and slide the Vertex through the Edge you want like a knife in butter to where you want it to be. Works like a glove.
Press E
E to extrude from the current vertex selected. You can do this repeatedly to create a long chain.