adjective behind a noun

[hotapplepie]

Hello, :)
I want to ask about adjective usages.
first, I want to list some examples to help discuss.
1.The boy (who is) standing there is my friend.
2.The girl (who is) locked behind the door is crying.
3.The student (who is) interested writes his name on this paper.
The student (who is) involved writes his name on this paper.
4.This is a city (which is) famous for its foods.
5.The girl (who is) beautiful is my girl friend.

As I have seen in grammar books, the common examples for participle phrase
are like sentence 1 and 2. In sentence 1 and 2,"standing" and "locked" are verbals.I mean they represent some kind of actions,and they are not just being adjectives. But in sentences 3,"interested"and"involved" are totally adjectives,
though they also come from verbs,their meaning are more like adjectives.
And sentence 4 includes a adjective phrase "famous for its foods".

My question is sentence 5. I guess this is not correct because I haven't seen this before. Commonly we would say "the beautiful girl" instead of "the girl beautiful".But since sentence 3 and 4 is correct, why can't this be? some books say sentence 4 is correct because it's a "phrase" and not a"word",
describing it as a grammar rule. But in sentence 3 it is just a "word",and it is correct just because it is participle? And sentence 5 is incorrect because it is
not a participle? is this a rule that we can decide adjective is behind or before
noun?

I don't know if i am misunderstanding something,or there is some grammar
I don't know.If any concept above is wrong,please correct them. I hope you
could explain it to me.

Thank you very much! :)

[SoothingDave]

5 is incorrect. "Beautiful" is not a participle and it is not the introductory word of a phrase. It is just an adjective, so it belongs before the word it is modifying.

The sentences in 3 are not correct either. Certainly not the "interested" one.

[hotapplepie]

5 is incorrect. "Beautiful" is not a participle and it is not the introductory word of a phrase. It is just an adjective, so it belongs before the word it is modifying.

The sentences in 3 are not correct either. Certainly not the "interested" one.

Thanks for your reply.
But I don't get it in setences 3.
It is incorrect because "interested"and"involved" are words and not phrases?
does that mean that we don't concern whether it is a participle,
but we concern whether it is a phrase?
In other words,does that mean if it is a phrase we put it after noun,
and if it is a word we put it before noun without considering whether it is a participle?

[SoothingDave]

The student (who is) interested writes his name on this paper.

You can't omit the "who is" from this sentence. You can re-write it as "The interested student writes..."

If you look at sentences 1 and 2, you have phrases "standing there" and "locked behind the door."

In 3 and 5 you have "interested" and "beautiful." Just adjectives. Not phrases.