用wave good-by 和wave a greeting 造句 对某人挥手打招呼介词是什么?

兄台,我来帮你了,
没人回答的原因我想有两点,一是你问的这两个词组比较不常见.二是你木有悬赏分.不过,我来了,那这两条就不管啦.哈哈.
The boy waved goodbye to his family and began his journey alone.
少年同自己的家人挥手告别,踏上了自己一个人的路途.
On seeing her mother,the little girl waved a greeting and said:"mum,i'm back"
一看到妈妈,小女孩儿就马上挥手跟妈妈打了个招呼,说道：“妈妈,我回来啦”
给某人挥手打招呼用的介词是to,如第二个例句里所示.