Definitions of engage
if you engage somebody in conversation then you start speaking with him or her
He engaged Mr. Skinner to survey the property.
if you are engaged in/on/upon something then you are doing that thing or are involved in a particular activity
The defendant needs to prove that there exist persons who were engaged in similar conduct and were not prosecuted.
if you engage somebody to do something then you employ or get someone to do a particular job or task
The men engaged him in conversation before punching him.