Yes and no.
You do use "he's" for "he is" and "he has".
You do use "he's got something" for "he has got something."
You do not use "he's something" for "he has something." [Note that according to @Optimal Cynic this is allowed in some parts of the world]
Therefore the first two sentences you proposed are correct:
He's angry.
He's been angry.
But the third one is incorrect. You cannot shorten "he has a house" to "he's a house." You can only shorten "he has got a house" to "he's got a house." [Again, note what @Optimal Cynic claims]
More examples:
Correct: I have an apple.
Correct: I have got an apple.
Correct: I've got an apple.
Incorrect: I've an apple.
Yes. He's can mean either he is or he has depending on context. She's and it's work the same way. Pick any reference.
- http://dictionary.cambridge.org/dictionary/american-english/he-s
- http://www.merriam-webster.com/dictionary/he's
- http://oxforddictionaries.com/definition/he%27s?q=he%27s
do we say "he's" as the contraction of "he was" | WordReference Forums
Can you omit “is” outside of “he’s” or “she’s”?
Are the contractions of "he is" and "he has" pronounced the same?
Is 'd (I'd, you'd, he'd...) only a contraction of would? Or can it also be a contraction of other words that end with -d, such as could, should or had?
It's both "had" and "would."
"You'd think it would be simple." (Would)
"He'd seen everything." (Had)
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“He’s” and “she’s” are correct contractions, but can the same be said for any noun+is, or are these two words exceptions?
For example, “John is a cool dude” would become “John’s a cool dude”. I say and hear “is” being shortened/omitted on the regular, but can this be put into writing? I try to avoid contractions in formal writing anyway, but would it be grammatically incorrect if I said/wrote “John’s” like in the example?
Also, semi-related question, but would it be correct to say that some words are “abbreviated” in contractions?