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Typically, stories can be divided into sections. Freytag's triangle, or pyramid, illustrates them:
The exposition, or the part where all the main characters and the main conflict are introduced. In "The Necklace, this would be when the reader sees Mathilde Loisel's desire to rise to or be accepted in a social class that is above her husband's means.
Rising action follows. This is the part of the story that leads up to the climax. This is the chain of events that is caused by the initial conflict. In this story, I think the rising action includes the invitation to the ball and Mathilde's visiting her rich friend, Madam Forestier, and borrowing what she believes is a very expensive necklace to go with the expensive dress she convinces her husband to buy for her. It may also include her appearance and her reception at the ball. This event highlights the sharp contrast between the life Mathilde wants and the life she is later forced to live as a consequence of her selfish choices and pride.
The third section is the climax, or turning point. It is also the point where the initial conflict (but not the only conflict necessarily) is resolved. This occurs when Mathilde realizes the necklace is missing. The initial conflict is over. From this point on, Mathilde no longer has a chance to blend in with high society.
The climax is followed by the falling action, which consists of the events that occur as a result of the climax. Mathilde and her husband must take a cheap apartment and work themselves into premature aging to pay for the lost necklace.
The last part of the story is the denouement, or resolution. This is the part where all the tangled conflicts are untied. the word denouement literally means unraveling. A more American interpretation would be to say the loose ends were all tied up. Mathilde runs into her old rich friend who still looks young and beautiful. She tells her how she worked to replace the necklace, and learns that she wasted her life for nothing, since the necklace she lost was fake.
For a graphic representation of the parts of a story, I am adding a link to a page the shows Freytags triangle/pyramid. I am also including a link to enotes summery of the story and some information on Gustav Freytag, the author and critic after whom the pyramid is named.
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