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Her behavior may be triggered by social anxiety/or being shy/introverted. If there is anyway to elicit from her the reason for her behavior, it would give you something solid to work with.
You can encourage her to wave hello to others initially, and then continue to prompt her to say it (verbally) Try to see if for some time at least she agrees to the waving.
At home, you can stage some play with her (you can use dolls or puppets) and pretend to exchange greetings. You can switch roles, she can say hi and you don't (and ask her how that feels)
Also, you can read to her or make up stories about polite girls.
Ward K. Swallow (Author)