Which geometric concept is associated with balance and similarity in shapes?

The geometric concept that is associated with balance and similarity in shapes is symmetry. Symmetry refers to a situation where one shape becomes exactly like another if you flip, slide, or turn it. It embodies the idea of balance because when an object is symmetrical, there is a sense of equilibrium in its shape and structure.

For example, if you have a butterfly, its left and right wings are mirror images of each other, demonstrating symmetry. This can also relate to similarity since symmetrical shapes often maintain the same proportions and angles, implying a consistent relationship between their dimensions.

While scaling involves changing the size of a shape while maintaining its proportions, and congruence refers to shapes that are identical in size and shape, neither of these concepts specifically conveys the idea of balance that symmetry does. Proportion discusses the relative size of different parts of a whole but does not inherently include the aspect of balance found in symmetry. Therefore, symmetry is the most fitting association with balance and similarity in shapes.