What kind of verb is the word "run" in the sentence "It's a shame cities aren't run like this." ? I think it's a past participle, but correct me if I'm wrong.
"run" in this context means "manage". It refers to the management of the city but I'm guessing you know the meaning already
It is not the past participle. It is the passive form. There is no need to mention the "doer" of the action because it is already understood OR it is not important.
NOT A TEACHER
(1) Active: The authorities do not run cities like this.
(2) Passive: Cities are not run like this (by the authorities).
(3) It is a shame (that) cities are not run like this. = It (that cities are not run like this) is a shame.
(a) I believe that "cities are not run like this" is a noun clause in apposition with "it."
(b) If you said, "It is a shame," your listener, of course, would ask: What is a shame?
You would reply, "Oh, that cities are not run like this [is a shame]."
The passive is formed with the verb be (or get) + past participle, so how is run not the past participle?
Your answer is wrong. Please do not answer questions incorrectly. The passive form here is aren't run and run is a past participle.