How can you deliver checkmate with a king?

Except that's your own personal interpretation. That's not what the rules say. Try playing in a tournament where you get to to use your own personal interpretation and not the official rules of chess for that tournament.

Read verb definition 3 here.

All those definitions seem perfectly reasonable. The act of positioning the rook where it is would be part of the checkmate. Even the knight, bishop and king are positioned well. But only one piece is actually checking the king, and that is the rook.

Through a revealed checkmate; you move your king and another piece has its attack revealed in a checkmate. You can't checkmate your OWN king by moving it though, that's impossible.
Edit: 26 days old topic, missed that.

Again I get what you are saying. You are saying that the last move is the one that results in checkmate, which is true. But that is not how the rules say check (or checkmate) work. The rules do not care what the last move was, they only care about the piece that is attacking the square the enemy king occupies.

Just because Bg4# was the last move does not mean the bishop is attacking the square the enemy king is on. The final position is what it is because the rook is attacking the square the enemy king occupies and the enemy king cannot escape. That is the checkmate position. Whether it was discovered check, promotion, en passant, etc doesn't matter. The last move of the game does not determine which piece is checkmating the king. As your diagram shows. The bishop is quite literally incapable of checking the black king. Its impossible.

Again, you are referring to checkmate as a position. We are talking about the action of checkmating, which is always done by the moving piece. For example, if you open the door for another person, you allowed them to go through the door.

That is incorrect. The last move reveals an attack that is checkmate of the king. So indeed that last move DOES actually determine which piece is checkmating the king. Because if that last move had not been made then the king would not have been checkmate by the revealed attack.

You're saying that it's true that the last move is the one that results in checkmate, which I agree with. So, since the definition of checkmate as a verb is to cause checkmate, then the last move is the one that checkmates. Meaning the piece that moves in the last move is the one that checkmates.

yup, she thinks that in the diagram below the rook checkmates, even though itt's obviously the bishop.

Yeah, and that's just how the rules are. The piece that makes the move is the one who causes (DETERMINES) what happens. So the Bishop causes the checkmate by revealing the Rooks attack.

and, therefore, takes the action of checkmating.

this is a very famous example of a king move checkamte.

Yes exactly, sorry, I was not being clear. I totally agree.

naaaa the bishop moved so the Rook could take all the glory... you could look at it as the bishop gave a sweet assist to the rook.

animated examples for ya'll....guess which one is the bishop...lol

Well I'm having a hard time reconciling your comments. If the last move reveals an attack, then that attacking piece that was revealed is the checkmating piece. Because the piece that attacks the square the king occupies is the checking piece. I think the key phrase is revealed attack. In our diagram the bishop is not attacking, therefore it cannot check (or checkmate). The revealed piece, the rook, is the attacking piece. Therefore it is the checkmating piece.

Actually no. The rules are this....

4. Objective and Scoring 
4A. Checkmate.
The objective of each of the two players in a game of chess is to win the game by checkmating the opponent’s king. 
A player’s king is checkmated when the square it occupies is attacked by one or more of the opponent’s pieces and 
the player has no move that escapes such attack. See also Rule 12, Check; 12C, Responding to check; and 13A,

The bishop is not attacking the enemy kings square, therefore it cannot be the checking or checkmating piece. The revealed piece, the rook, is the piece that is attacking the square the king occupies. Those are the rules.

Except the rules DO specify which piece is checkmating. It's the piece that is attacking the square the enemy king occupies. In our example, that certainly isn't the bishop, as that would be impossible (different colored squares). The rook is the piece that is attacking the square the enemy king occupies, therefore, according to the rules of chess, it is the checkmating piece.

Where does it say that? Please provide a link to your source.

I just did. USCF 4a

I copied the exact rule concerning checkmate.