The Kurdish language belongs to the western sub-group of the Iranian languages which belong to the Indo-Iranian branch of the Indo-European languages family. The most closely related languages to Kurdish are Balochi, Gileki and Talysh, all of which belong to the north-western branch of Iranian languages. Persian which belongs to the south-western branch, is also considered a related language, however the differences between Kurdish and Persian are far stronger than the similarities.

http://en.wikipedia.org/wiki/Kurdish_language

Turkish is a member of the Turkish family of languages, which includes Gagauz and Khorasani Turkish. The Turkish family is a subgroup of the Oghuz languages, themselves a subgroup of the Turkic languages, which some linguists believe to be a part of the Altaic language family.

http://en.wikipedia.org/wiki/Turkish_language