Do not disturb a sleeping dog.  Here 'sleeping' is -

• Do not disturb a sleeping dog.  Here 'sleeping' is -  Present Participle.
• Participle:
- It is the form of a verb that usually ends in "ed" or "ing" and is used as an adjective:
- Participle একই সাথে Verb ও Adjective এর কাজ করে। 
• Participle মূলত: তিন প্রকার: 
1. Present Participle. Ex: Do not disturb a sleeping dog. 
2. Past Participle. Ex: This is a book written by Charles Dickens. 
3. Perfect Participle. Ex: Having eaten rice, he went to bed.