The same thing works for guessing German grammar from English. The farther back you go in English, the more its grammar resembles German.
"What sayest thou?" -> "Was sagst du?"
In fact, for the above, you don't even have to know a single German word. You just have to know what for question words, "wh" -> "w", that the English "y" at the end of a syllable usually comes from an older Germanic "g" sound, and that "th" was replaced by "d" in German. That gets you 90% of the way from early modern English to modern German in the above example.
That's interesting. I haven't thought about it in that direction before. I'm "of course" aware of the High German consonant shift, which also muddled things a lot (the continuum around to North Sea is a lot "cleaner" if you look at Plattdeutsch instead), but never thought much about what other simple transformations to apply with standard modern German.