It's not just "like" the Northern offshoot of Germanic, they are North Germanic languages, like English is a West Germanic language.
The similarity is even stronger if you compare with Low German (most common in the North), which didn't go through the consonant shift of the now dominant High German (e.g. day: Norwegian dag vs. Low German Dag vs. High German Tag)
The similarity is even stronger if you compare with Low German (most common in the North), which didn't go through the consonant shift of the now dominant High German (e.g. day: Norwegian dag vs. Low German Dag vs. High German Tag)