These are all indo-european languages. It's not like Sanskrit was imported into these languages, but Sanskrit along with most European languages share a common ancestor, from which they all started to diverge thousands of years ago.

https://en.wikipedia.org/wiki/Proto-Indo-Europeans

Here's a visualization of IE languages, perhaps not accurate in every single detail, but easy to remember:

http://mentalfloss.com/sites/default/files/196.jpg