Does threefold repetition apply in a rapid game? I had a winning position in a 10+5 OTB game, but I was low on time. I repeated position to gain some time. My opponent stopped the clock and claimed a draw. The arbiter was called, ans ww agreed that the position had been repeated three times. The game was judged a draw. I protested as I didn't think this rule apply to rapid chess. Who is correct?
TL;DR: Claiming draws based on threefold repetition or the fifty-move rule is possible in rapid and blitz games as well. Contrary to RemcoGerlich's answer, it is not strictly necessary to record the moves to be able to claim a draw.
Note: This is based on the version of the Laws coming into effect after 1 July, 2017. However, as I am not aware of changes afffecting my reasoning, the following also applies since at least 1 July, 2014.
In rapid and blitz games, the tournament rules apply unless a certain rule is abrogated by the Appendices A and B for rapid and blitz games, respectively.
Up to July 2014, the rules made this very obvious (A.4 for rapidplay):

Where supervision is inadequate the Competition Rules shall apply, except where they are overridden by the following Laws of Rapidplay:
[...]

This provision has disappeared from the rules, but it is clear that this interpretation still holds.
Claims of draw by threefold repetition are covered by Article 9.2.1 of the Laws of Chess:

9.2.1 The game is drawn, upon a correct claim by a player having the move, when the same position for at least the third time (not necessarily by a repetition of moves):
9.2.1.1 is about to appear, if he first writes his move, which cannot be changed, on his scoresheet and declares to the arbiter his intention to make this move, or
9.2.1.2 has just appeared, and the player claiming the draw has the move.
9.2.2 Positions are considered the same if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same. Thus positions are not the same if:
9.2.2.1 at the start of the sequence a pawn could have been captured en passant
9.2.2.2 a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost only after the king or rook is moved.

Let's not forget the paragraph immediately preceding article 9.2.1, applying both to threefold repetition and the fifty-move rule:

9.1.2.3 A claim of a draw under Article 9.2 or 9.3 shall be considered to be an offer of a draw.

Therefore, if a claim is made in accordance with the rules and the position has in fact appeared on the board for the third time, the arbiter must declare the game drawn. (I would argue even if the player does not write down the move he intends to make the arbiter should declare the game drawn. See below.)
Note that if the opponent of the player claiming the draw

agrees to the implicit draw offer
or agrees that a threefold repetition has, in fact, occured on the board,

the arbiter may declare the game drawn without further inquiry.
Really nitty-gritty nitpicking: If the claim has not been made in a formally correct way and the opponent agrees that a threefold repetition has occured or if both players wrongly agree the same position has occured three times, technically, the rules demand that the game is to be continued.
If neither of these criteria are met, the claimant has the burden of proof. In my opinion (other arbiters may disagree), the arbiter needs to be presented with &quot;clear and convincing evidence&quot;, to use legal terminology, to determine the game drawn. Clearly, a correctly filled out scoresheet usually meets this standard of evidence.
However, the arbiter may also convince himself using other sources of information available to him. The following cases come to mind:

As mentioned by RemcoGerlich, if the arbiter has been observing the game for a while (e. g. because it is the last game of the current round), he may conclude that a threefold repetition has occured. However, he may only intervene upon a correct claim of the players.
If the game is played on an electronic chess board, the arbiter may certainly use the information provided there. (Even in normal games, I sometimes deem it necessary to check a claim using the livechess software.)
The arbiter may ask neutral, objective bystanders. However, he has to be sure about their objectivity and understanding of the game.

Regarding the provision &quot;[...] if he first writes his move, which cannot be changed, on his scoresheet and declares to the arbiter his intention to make this move [...]&quot;:
Many players and even arbiters will agree that following the procedure to claim a draw correctly can be quite complicated. The reason is that these rules ensure that the opponent will be distracted as little as possible. This is why you may not claim the draw when your opponent has the move. You are required to write the move down on the scoresheet as an indication that you intend to play that move. In rapid games, you usually don't write moves down. However, I would argue that clearly communicating your intent to the arbiter in those cases may be considered sufficient for a claim. In the new rules, this is made explicit by article A.2:

Players do not need to record the moves, but do not lose their rights to claims normally based on a scoresheet. [...]

Even in the past, this has been the usual interpretation of the rules, at least in the German-speaking chess community. A similar case appeared in the German Bundesliga back in 2009. The final decision (in German) can be found here. Even though the player claiming the draw (a grandmaster) had neither stopped the clocks nor written down the move on his scoresheet, the deciding body ultimately ruled that the player clearly conveyed his intent to claim a draw by making a certain move and declared the game drawn.