balance vs symmetry

balance and symmetry both are nouns.

Word	Noun	Adjective	Verb	Adverb
balance	Yes	No	Yes	No
symmetry	Yes	No	No	No

As nouns, balance and symmetry are synonyms defined as:

balance and symmetry: (mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane

Other synonyms of balance include correspondence, symmetricalness.

As nouns, symmetry is a hyponym of balance; that is, symmetry is a word with a more specific, narrower meaning than balance:

Other hyponyms of balance include conformation, proportion.

balance (noun)	symmetry (noun)
a scale for weighing; depends on pull of gravity	(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane
a weight that balances another weight	(physics) the property of being isotropic; having the same value when measured in different directions
a wheel that regulates the rate of movement in a machine; especially a wheel oscillating against the hairspring of a timepiece to regulate its beat	balance among the parts of something
harmonious arrangement or relation of parts or elements within a whole (as in a design)
(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane
equality between the totals of the credit and debit sides of an account
the difference between the totals of the credit and debit sides of an account
something left after other parts have been taken away
equality of distribution
a state of equilibrium

balance (verb)	symmetry (verb)
hold or carry in equilibrium
compute credits and debits of an account
bring into balance or equilibrium
be in equilibrium