In other words, it is a self-congruence.
Intuitively and informally, a symmetry is a movement of the figure so that it looks exactly the same after it has been moved.
- Results about symmetry mappings can be found here.
The word symmetry comes from Greek συμμετρεῖν (symmetría) meaning measure together.
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): $\S 2$: Example $2.5$
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Definition of Group Structure: $\S 26 \eta$
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 34$. Examples of groups: $(5)$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: symmetry (of a geometric figure)