Equality is a relation (in first order logic). It is an axiom of Peano arithmetic, that equality is SYMMETRIC
i.e. for all a and b if a=b then b=a.
In geometry, symmetry is likewise considered a property of equality. It is part of the definition of the equals relation, or an axiom, not something to prove. It is this way in any well-known axiom system of first order logic, or easily proven to be symmetric if it is defined in terms of something itself symmetric.