Answer:
Dialogue, in the last sentence, "Shelly started a dialogue with her coworkers about how to handle the problems the company was facing." actually uses the word correctly.
Step-by-step explanation:
In the other sentences, the words prologue and dialogue are being mixed up.
For example: The first sentence uses dialogue instead of prologue, which doesn't make sense for the context of the sentence. And the second sentence uses prologue instead of dialogue.
Hope this helps ya :)