Yes, I know I technically used the word wrong. But it wouldn’t be funny otherwise.
See, the word pact has an amazing range of relatives. And I’m not talking about the obvious ones like compact and the above mentioned impact. I’m talking about pale, page, peace and fang. Yes really!
It’s due to all the words’ ancestry. Pact itself comes from the Old French pacte and the classical Latin pactum, both of which meant a contract or agreement of some sort. Pactum is the past participle (basically, the past tense) of pacisci, which can be traced to the Proto-Indo-European pag—join together—not unlike what a pact does in the metaphorical sense
Pag is the thread that ties all the words together. The older, no longer widely used definition of pale is a fence post (hence impale, to pierce with a stake). In Latin, it was palus, stake or pole, which is related to the “fix or fasten” definition of pangere, another descendant of pag. And obviously the same goes for the far more common impale, where the im- prefix is added to make it something like “staked upon.”
That pactum-pangere-pag has a lot more (ahem) impact. Impinge (which I swear I did not have to look up before writing this post) used to mean “fasten forcibly” or “come into violent contact with.” It’s from the Latin impingere(“push into”) and it’s past participle is impactus. And I’m sure you can guess what word that’s the origin for. Like the above, the words are from pangere. Compact follows a similar line, just with a prefix that means with or together. However, the Latin compact compactus actually means concentrated. Since something that is compacted can be considered concentrated in a small area, that makes sense.
Okay, now it’s time for the weirder words. Peace isn’t related to pangere or pag, but it is related to pacisci—an agreement—which comes from another Proto-Indo-European word: pak (it means fasten…similar, right?). The sense of the word comes from the idea of a peace treaty, a stopping of war. Page might also seem odd, but that’s only because when it was the Latin pagina (from pangere, of course) it meant a “strip of papyrus fastened to others.” So pagina is like saying a fixed piece of paper. But the weirdest word here is probably fang. Unlike the rest of the words, fang comes from Proto Germanic, not Old French. The word there was fango, which comes from our old friend pag. Why’d they choose that word for a tooth? Because its Old English equivalent is fengtoth, a catching or grabbing tooth.
TL;DR: All these words are like third or fourth cousins. It’s hard to see the resemblance, but they do have relatives in common.
Online Etymology Dictionary, for all its interesting facts
Dictionary.com, because come on. How often do you use impinge?