We have a promising genetic cousin match at 23andMe. We'll call him J.D. He matches both my father and my father's third cousin, which quite a few people do. The difference is that the match, or the identical segment of DNA, is the same among J.D., my father, and our third cousin! Perhaps triangulation describes this scenario?
Here is what the graph looks like:
The common ancestors shared by my father and his third cousin are their great great grandparents, Calvin Cook and Mary Neil. They were born around 1830 and lived in Morris and Hudson Counties in New Jersey. We do not know at this point if the shared DNA on chromosome 13 is from Cook or Neil. We need to go back in time in both trees and we should find an ancestor in common with J.D. We do not know how many generations back we must explore until we find a common ancestor. All we know right now is that the match is through Calvin Cook's line or Mary Neil's line, which greatly narrows our search.
This illustrates why you need document-based genealogical research to help you with DNA genealogy.
Compare the above graph to this graph. A. D. matches both my father and his third cousin, but on different chromosomes. We cannot determine with this information if the double matching indicates a single common ancestor.