Pick any language you want and trace it back to its roots. They will eventually merge with the roots of other languages. This holds true for Persian and English as well as languages like German. The Persian language family specifically is a branch of the Indo-European languages, a branch of which is Germanic language family. English happens to be a member of the Germanic languages. So what we found is that Persian and English do indeed have the same origins (which is expected since as far as we know, all languages go back to one single language). So the next logical step now is to find out whether the word "mother" sounds the same in Persian and English because of their similar roots, or if it's just a coincidence.
As it turns out, this actually is because of their similar roots, as stated by Google : Old English mōdor, of Germanic origin; related to Dutch moeder and German Mutter, from an Indo-European root shared by Latin mater and Greek mētēr
This is also the case for the word "brother". You get the idea .