Praise be to Allah.
It is not permissible to greet with a wave of the hand, rather the Sunnah is to greet and return the greeting with words. Greeting with a wave of the hand is not permissible, because it is an imitation of some of the kuffaar who do that, and because it is contrary to what is prescribed by Allaah. But if a person gestures to the one whom he is greeting to indicate that he is saying salaam, because he is far away, whilst also uttering the words of the greeting, there is nothing wrong with that, because there is evidence to that effect. Similarly, if the person who is greeted is busy praying, he may respond with a gesture, as was narrated in the saheeh Sunnah of the Prophet (peace and blessings of Allaah be upon him).
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