What words complete this analogy request and entreat?

The words that complete the analogy "request : entreat :: ___ : ___" are ask : implore.

Here's why:

* Request and ask both imply a polite or formal way of seeking something.

* Entreat and implore both suggest a more urgent or pleading way of seeking something.

Therefore, the analogy shows a progression from a more casual to a more intense way of making a request.