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To wave one's arms to attract someone's attention, usually to get them to stop moving. A noun or pronoun can be used between "flag" and "down." I was finally able to flag down a passing motorist to help with our stalled car. It'll take awhile to flag a taxi down. Why don't we just walk to the museum?
flag someone or something down
to signal or wave, indicating that someone should stop. Please go out and flag a taxi down. I'll be right out. She went to flag down a taxi.
Signal to stop, as in The police were flagging down all cars. This expression uses the verb flag in the sense of "catch the attention of, as by waving a flag," a usage dating from the mid-1800s; down was added in the first half of the 1900s.
To signal something or someone to stop: I flagged down a taxi when it started raining. When we ran out of gas, we flagged the police officer down to ask for help.