Two things are compatible when they work together without a fight. The charger fits the phone; two flatmates share a kitchen for two years and never once argue about the bin.
The preposition is with, every time: compatible with. Computing has taken over much of the word — a file compatible with older versions, a compatible printer — but the older jobs are all still there. People are compatible, and so are blood types. A statement can be compatible with the evidence, meaning it does not contradict it: his account is not compatible with what the neighbours saw. The opposite is incompatible and the noun is compatibility. Compatible is not the same as similar, since two very unlike people can be compatible, which is half the point of the word.
1adjectivecompatibleAble to exist or work together without conflict.
“The two of them turned out to be more compatible than anyone expected.”
2adjectiveequipmentOf equipment or software, able to be used together with something else.
“The app is compatible with phones going back six years.”
3adjectiveconsistentConsistent with something; not contradicting it.
“The timings are not compatible with his version of events.”
The Medieval Latin compatibilis was a church lawyer's word: two benefices were compatibilis if one man could hold both at once. It was built from com-, together, and pati, to suffer, so compatible people are at root people who can suffer together. The same pati sits inside patient and passion.
Latin
compator — to suffer with
Medieval Latin
compatibilis — in compatibile beneficium, a benefice which could be held together with another one
Anglo-Norman
compatible
Middle English
compatible
English, today
compatible
Built from
Middle English compatible, fron Anglo-Norman compatible, from Medieval Latin compatibilis (“in compatibile beneficium, a benefice which could be held together with another one”), from Latin compator (“to suffer with”), from com- (“together”) + pati (“to suffer”); see passion.
Etymology from Wiktionary, CC BY-SA