antworten = to answer (--> you give an answer to a question) erwidern = to reply (--> you don't agree with something and express your opinion) ansprechen = --> 1. you want to start a conversation with someone/ 2. you want to discuss or clarify something --> but by the way the Adjective "ansprechend" = you are attracted to something I hope it helps =)

The verbs antworten, erwidern (and also entgegnen) can be used interchangeably. There's no difference in meaning. Regarding ansprechen it depends on the context: Jemanden ansprechen can simply mean to start a conversation. It can also mean just asking. (Wenn ich ihn das nächste Mal sehe, werde ich ihn darauf ansprechen.) And it can mean as much as remind someone. (Bitte sprechen Sie mich morgen noch mal darauf an!) Etwas ansprechen means to bring up a topic in a conversation. Used in negation ansprechen can also express a certain dislike or disapproval. (Dieser Film spricht mich überhaupt nicht an.)