正式文体中：engage sth, 成功地吸引住注意力，兴趣，并长久地保持。It is a movie that engages both the mind and eye, 这是一部赏心悦目的电影；
正式文体中：engage sb as sth, 雇用，聘用。He is currently engaged as a consultant. 他现在受雇为顾问；engage sb to do sth. 雇用某人做某事。Her parents engaged a professional worker to paint their new house. 她父母找了一个专业的工人来粉刷他们的新房子；
engage with sth/sb. 与。。。建立密切的联系，尽力理解。She has the ability to engage with young minds. 她能够与年轻人心意相通；I tried my best to help my students engage in the new curriculum, but I failed. 我努力使我的学生理解这个课程，但我失败了；
正式文体中：engage sb, 与某人交战，开战。It is not surprising that he finally engaged the ememy for his beloved girl. 他最终为了他心爱的女孩与敌人展开殊死搏斗一点也不为吃惊。
机械之间的衔接，咬合。The cogwheels are not engaging. 齿轮未咬合在一起；engage with sth. One cogwheel engages with the next. 齿轮一个个咬合在一起；
engage in sth. 使从事，使参加。Even in prison, he continued to engage in criminals. 他甚至在监狱里还从事犯罪活动；
engage sb in sth. She tried desperately to engage him in conversation. 她想尽办法要他跟她谈话；engage sb in doing sth. The teacher successfully engaged more students in joining in the activity. 老师成功地让更多的学生参与到这个活动中来。
希望对你有用。