Using the baseline characteristics of the mystery, as established in class, identify the aspects of "Murders in the Rue Morgue" which allows this story to be classified as a mystery.

Two fundamental characteristics of the mystery story are a suspenseful plot that raises lots of questions and mysterious, intriguing characters who might help the reader to answer those questions. Edgar Allan Poe's "The Murders in the Rue Morgue" demonstrates both of these characteristics.
The first and most important characteristic of a mystery story is a suspenseful plot. The first moment at which suspense is introduced into the plot of "The Murders In The Rue Morgue" is when we hear of the gruesome murder of an old woman and her daughter that the police are unable to solve. Part one of the story ends with a cliff-hanger, when the narrator says, "Dupin . . . knew what to do."
The suspense is raised in part two, when we discover that the door and the windows of the room that the old woman's daughter was found dead in were all locked from the inside and covered in blood. The question as to how the murderers escaped becomes the heart of the mystery. There are, however, other questions that contribute to the mystery, such as why the murders were so violent, and what the motive could possibly have been.
Another key characteristic of a mystery story is intriguing, peculiar characters. Dupin certainly qualifies as just such a character. The narrator, early in the story, says that there are

two Dupins—one who coldly put things together, and another who just as coldly took them apart.

The repetition of the word "coldly" might be intriguing here and perhaps ominous. Dupin seems like a peculiarly calculating character. In fact, he has preternatural powers of deduction, which seem to point to an ability to read minds. As well as being an intriguing character, very much the predecessor of Arthur Conan Doyle's Sherlock Holmes, Dupin also adopts the role of the story's detective.
This character role is also an important part of the mystery story. The detective character is someone who the reader can follow as they uncover the central mystery. We see the mystery from his or her perspective, ask the same questions, and are guided to logical, if unexpected, answers. Dupin fulfils this role very well and guides us to the revelation at the end of the story.