As an English-speaking student of Yiddish, I was pleasantly surprised to discover that the indefinite article was an before vowels and a before consonants, just like in English. But as far as I can tell, Yiddish developed this independently from English. That is, both turned the Proto-German *ainaz ("one") into two separate words, the number one (eyn in Yiddish) and an indefinite article which is identical in the two languages.
Are there any other examples of two languages which shared a root, separated, and ended up with nearly identical words much later, despite otherwise diverging considerably?