An intrinsic property of a mathematical object which causes it to remain invariant under certain classes of transformation.

• A. Invariance
• B. Symmetry
• C. Congruence
• D. Identity

Answer: (B)

Symmetry is an intrinsic property that makes an object look the same after applying certain transformations, like rotations or reflections. When an object has symmetry, it remains unchanged under those transformations, which is exactly what we mean by invariance. Invariance describes the state of staying the same, but symmetry explains why that happens. Congruence is about two shapes being the same under rigid motions, not about a single object's property causing it to stay the same. Identity is just the notion of being the same object as itself, not a broader invariant feature. So the best answer is symmetry.