用到比较多的含义是：订婚，使参与
还有这个
to interest someone in something and keep them thinking about it
吸引住，使感兴趣
The debate about food safety has engaged the whole nation.关于食品安全的争论引起了全国关注。
If a book doesn't engage my interest in the first few pages, I don't usually continue reading it.如果一本书的前几页不能引起我的兴趣，通常我就不再往下读了。
不过最近我看之前的一篇高考完形填空，因为把它改编成了一篇读后续写2020年7月浙江高考完形填空改编成读后续写：My dog stole my tractor
其中原文中有这么一句：
Lamb and mother reunited, I turned back to the tractor only to see it move suddenly away from me. This was so unexpected that it took me a moment to process what was happening. I’d put the handbrake on when I jumped out, as I always do, and I knew Don wasn’t able to release it – had it not engaged properly? I still don’t know how, but it was clear that Don had somehow set the vehicle in motion. He was watching me, without any obvious concern, as the tractor careered away.
这里，engage就有了新的含义
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