Mourners are forbidden to greet people (lit., “seek the peace of others”) (Sh.A., Y.D. 385). Likewise, one may not extend greetings to others on Tish’a B’Av (Sh.A., O.C. 5554:20). [After all], just as a person who has lost a close relative is not in a state of “peace,” no one is in a state of “peace” on Tish’a B’Av, because we are mourning the destruction of our Holy Temple.
In particular, Torah students who know the halachah must be careful in this regard. However, when a person unfamiliar with the halachah extends greetings to another, the recipient should return the greeting in a soft voice and serious tone, as one who is preoccupied with thoughts of mourning and sorrow, making sure not to insult the person in the slightest. It is preferable to answer, “Good morning,” and avoid saying, “Shalom” (“Peace [unto you]”). If the person who initiated the greeting is someone who wants to learn Torah, and there is no concern that he will be insulted, one should explain to him that we do not greet each other on Tish’a B’Av.
According to most poskim, one is even forbidden to say, “Good morning” or “Good evening (M.B. 554:41, K.H.C. 90). Some say that only the word “Shalom” is forbidden, while phrases like “Good morning” are permissible (Leket Yosher). We already mentioned that when necessary – in order not to insult someone – a person may return a greeting; and since some hold that “Good morning” and “Good evening” are not included in the prohibition, it is preferable to use these phrases than to say, “Shalom.”
One who meets a friend who just got married or had a child may wish him a “Mazal Tov,” for giving someone a blessing is not included in the prohibition of extending a greeting (Piskei Teshuvot 554:19). Similarly, hand shaking is not included in the prohibition (Har Tzvi, Y.D. 290).
Just as one may not offer greetings on Tish’a B’Av, one may not send gifts either (M.B. 554:41). Charity, however, is not considered a gift. Therefore, one is permitted, even obligated, to send food to the needy, so they can have something to eat after the fast (see K.H.C. 554:91).