Obrigado vs. obrigada
In Portuguese, the words for thank you, obrigado and obrigada, are chosen based on the gender of the person who is speaking or expressing gratitude. The word literally means obliged, so it must agree grammatically with the speaker.
Obrigado
A1This word is used by a male speaker to say thank you. A man uses obrigado because the word, being an adjective, must agree with his masculine gender.
Aqui está sua encomenda, senhor. — Muito obrigado.
(Here is your package, sir. — Thank you very much.)
Obrigado por me ajudar a consertar o carro.
(Thank you for helping me fix the car.)
Quer mais suco? — Não, obrigado, já bebi o suficiente.
(Would you like more juice? — No, thank you, I have had enough.)
Fico-lhe muito obrigado pela sua gentileza.
(I am very grateful to you for your kindness.)
Obrigado a todos pela presença.
(Thank you all for being here.)
Obrigada
A1This word is used by a female speaker to say thank you. A woman uses obrigada because the word, being an adjective, must agree with her feminine gender.
Seu cabelo está lindo! — Obrigada, acabei de sair do salão.
(Your hair looks beautiful! — Thank you, I just left the salon.)
Obrigada por cuidar das minhas plantas enquanto eu viajava.
(Thank you for taking care of my plants while I was traveling.)
Gostaria de entrar para um café? — Obrigada, mas estou com pressa.
(Would you like to come in for a coffee? — Thank you, but I'm in a hurry.)
Estou muito obrigada pelo seu apoio.
(I am very thankful for your support.)
Obrigada, mamãe, por tudo o que você faz.
(Thank you, mom, for everything you do.)
Summary
In essence, the rule is simple and based on the speaker's gender. If you are a man, you always say obrigado. If you are a woman, you always say obrigada. This is true regardless of the gender of the person you are thanking.