grammar - Participial as adverbial?

1. ''Solve the questions using what I have taught you.''


2. ''He showed up wearing a suit.''


3. ''It is doing a nice job covering up the broken chair.''


4. ''I broke the law getting you out of jail.''


5. ''You were torturing yourself figuring out how to tell her.''

I can understand the meaning. But I don't understand why they are used without a preposition.

Are these participial used as adverbial? Or they are catenative verb?