Rory and Dean attend a Chilton dance together and confirm they're boyfriend and girlfriend.  Emily stays at Lorelai's to take care of her injured back and to see Rory off to the dance.  When Rory and Dean fall asleep and don't come home til 5 am, Emily thinks they had sex, causing another fight between Emily and Lorelai.

Gilmore Girls
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Gilmore Girls Season 1 Episode 9 Quotes

Dean: You said 'boyfriend'.
Rory: No! I just meant boyfriend in the sense that the whole defending me thing was very boyfriendy, but only in the broadest sense of the word, which doesn't even apply at all here.

Rory: Are you my boyfriend?
Dean: In the broadest sense of the word way?
Rory: No, in the real, 'Hi, this is Dean, my boyfriend' kind of way.
Dean: Well, I am if you want me to be