As we've seen this week, symmetry is a multi-faceted word. In its broadest sense, symmetry means balanced. In photography, this means that your photo is well-composed and that it has interest and movement throughout. How lines and light move through an image create balance. How a subject is placed in the frame with regard to negative space or background creates balance.
Find something that is both familiar and meaningful to you. Study it for a few minutes. Notice its shape. How does its look, change in different light or from another perspective? Photograph the object such that you create symmetry by way of balance. You may choose to include the entire object or only a part.
Whatever you do, create a meaningful image of something that is meaningful to you.