The Spanish pegar (“to paste”) comes from the Latin pix, meaning “tar.” That makes sense: “paste” looks like just a more diluated “tar.”
But pix itself comes from the Proto-Indo-European root pei(e), which meant, fat — think of animal fat, for example. It makes sense that this word evolved into a word meaning “tar”: that’s a bit what animal fat looks like.
From this same root pei(e), we get a few notable English words:
Pluma, Spanish for “feather”, sounds nothing like the English feather.
But it is a cousin to the English fleece.
Both come from the same Indo-European root *pleus‑, which meant “feather” or to “pluck.”
But they sound so different! That is because the Indo-European p- sound stayed the same into Latin then Spanish, but changed into a f- in the Germanic branch (including English).
Thus the p‑l of pluma maps to the f‑l of fleece.
Father is one of the most basic words in every language and a traceable pattern throughout the Indo-European languages.
The original PIE sound “p-” changed in all the Germanic languages to “f-”. This is referred to as “Grimm’s Law”, from the fairy-tale fabulist who first noted this pattern.
In the Latin languages such as Spanish, the original “p-” sound was preserved. Thus, the Spanish padre’s p‑d-r root maps to the English father’s f‑th‑r root.