Yes, SYMMETRY is a Scrabble word!

Letter values in Scrabble US: S 1, Y 4, M 3, M 3, E 1, T 1, R 1, Y 4.

Is it a valid word?

SYMMETRY is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane
balance among the parts of something
(physics) the property of being isotropic; having the same value when measured in different directions