1560s, "relation of parts, proportion," from Latin symmetria, from Greek symmetria "agreement in dimensions, due proportion, arrangement," from symmetros "having a common measure, even, proportionate," from syn- "together" (see syn-) + metron "meter" (see meter (n.2)). Meaning "harmonic arrangement of parts" first recorded 1590s. Symmetrophobia is from 1809, supposed to be evident in Egyptian temples and Japanese art.
symmetry sym·me·try (sĭm'ĭ-trē)
Exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis.