English and German: two daughters of West Germanic.
English and German descend from a shared western branch of Germanic. Follow the family tree in the research record, and see why its stages are conventions rather than birthdays.
Start with the branch
Ringe and Taylor's The Development of Old English, the second volume of A Linguistic History of English, traces the development of English sound and word structure from Proto-Germanic to Old English of about the year 900. Its early chapters cover the diversification of Northwest Germanic and West Germanic before turning to the separate prehistory of Old English. Oxford University Press ↗
A convenient subgroup
The research record treats West Germanic as a convenient genealogical subgroup and stage for western Germanic varieties. English and German each descend from it, with confidence 0.93 for each link, and Proto-Germanic sits above it at 0.94.
Stages are conventions
English is conventionally divided into Old, Middle, Early Modern, and Modern English, and German includes the historical development of High German toward the modern standard. Neither division is a date on which people began speaking differently.
Beyond the pair
Kapović's survey of the Indo-European languages places Germanic among the other branches, which is the right frame for asking how much English and German share and how much they share with, say, Slavic or Latin. Routledge ↗
A question to carry forward
If English and German are close cousins but neither descends from the other, what kinds of word would you expect to find in both, and what would suggest borrowing instead of inheritance?