''Without'' com o gerúndio (ing)

Hi there,

Every time you use a verb after the preposition "without" try and add "ing" to this verb:
Examples:
a)She left without saying anything to me.(Ela saiu sem dizer nada pra mim.)
b)They travelled without getting the visa.(Eles viajaram sem pegar o visto.)
c)It was rude of you to leave without even saying a word.(Foi grosseria sair sem dizer nada.)
d)We cannot make it without being humble.(Nao conseguimos vencer sem sermos humildes.)
e)Alizee never does a concert without taking the time to say hello to all her fans.(Alizee nunca faz um show sem tirar um tempinho pra cumprimentar todos seus fas.)

Best regards!