When you act treacherously, you betray someone. If you tell everyone in school your best friend's carefully guarded secret, you've behaved treacherously.
Acting treacherously hurts or deceives another person, or betrays a secret or promise. A little boy might treacherously give away his sister's hiding place during a game of hide and seek — and his sister, in turn, might treacherously announce to some older kids that he's scared of the dark. In both cases, a secret has been betrayed. Treacherously comes from the adjective treacherous, with its Old French root word, trechier, "to cheat or trick."