Just to further extrapolate, the climax is a totally separate plot element than the rising action and the falling action. Yes, the rising action LEADS to the climax (the highest point of tension in a story), but it is in no way part of it. Similarly, the falling action extends FROM the climax, but it is in now way part of it. All of these elements (including the others of the Freytag's Pyramid that the above editor mentions) join together to form a complete plot. Teachers often use this pyramid to teach plot and, most likely, they will expect that you will apply this new knowledge to the stories you will read in the future.
Freytag's Pyramid is used to explain the plot structure in a novel or in a play. Following are the different stages:
1.The Exposition:The writer introduces the characters and setting, providing description and background.
2. The Rising Action: The dramatist or the novelist introduces complications in his plot.
3. The Crisis: The moment of greatest tension in a story. This is often the most exciting event. It is the event that the rising action builds up to and that the falling action follows.
4. The Falling Action: The events which happen as a result of the climax.
5. The Ending: The character solves the main problem/conflict or someone solves it for him or her. At this point, any remaining secrets, questions or mysteries which remain after the resolution are solved by the characters or explained by the author.
The climax is also known as the 'crisis' and the 'rising action' refers to the episodes which come before it and the 'falling action' refers to the episodes which come after it.