How we change what others think, feel, believe and do
When we see symmetry, we assume there is some connection between the two parts. We may also assume that each of the two parts is a coherent whole.
In symmetry, shapes have an axis (the 'axis of symmetry'), either side of which is a mirror-image of the other. This axis can be at any angle, but it is most often vertical or horizontal.
Shapes can have vertical, horizontal or diagonal axes, as these examples show.
Symmetry is a form of similarity, which leads us to connect the two parts, creating them either as a single object or with one as a reflection of the other. The very fact of symmetry also tends to make each of the two parts a whole as we must conclude that each half is whole in order to fit it with the other half.
Symmetry creates a pleasing balance, where one side of the image matches the other. Reversal of the shape is 'the same but not the same' and so creates both harmony and tension.
More generally, symmetry is a form of order, which helps to make us feel good at discovering regular patterns. This boosts our sense of control, as finding patterns often means being able to predict how things are.
As a recognized pattern, symmetrical foregrounds stand out against asymmetrical backgrounds. This is one reason why people and animals (who have symmetrical bodies) tend to be more visible.
Symmetry is often found in art, where it may be obvious and it may be more subtle, with perhaps only hints of a reversed duplicate.
Mirrors have a particular fascination for us and ancient cultures considered the image somehow mysterious and magical. Of course seeing ourselves is a boost to identity. Reflections in water also are found pleasant and can be found in many photographs.
Use symmetry to draw attention to things where you want the other person to focus. Make the background asymmetrical or plain to exaggerate this effect.