engage的名词是engagement。
engagement
[英][?n?ge?d?m?nt][美][?n?ɡed?m?nt]
n.
约会; 订婚，婚约; 约定，契约; 雇用;
复数：engagements
例句
1、Perhaps because you gave her an engagement ring?
或许是因为你给了她订婚戒指吗？
2、Where do the rules of engagement end and the crimes begin?
交战规则在哪结束罪行又从何处开始呢?