Two types of bilateral symmetry in the Metazoa: chordate and bilaterian.

The chordate sagittal plane is perpendicular to the sagittal plane primitive for the bilaterally symmetrical metazoans (Bilateria). The earliest metazoans, when symmetrical at all, were probably radial in symmetry. The axis of symmetry was vertical and the mouth, when present, opened either upward or downward. The Bilateria evolved from the primitive metazoan condition by acquiring bilateral symmetry, mesoderm, a brain at the anterior end and protonephridia. Perhaps in the stem lineage of the Bilateria a hydroid-like or medusoid-like ancestor fell over on one side onto a substrate (pleurothetism). If so, the anteroposterior axis of Bilateria would be homologous with the vertical axis of radial symmetry in coelenterates. The bilaterian plane of symmetry arose to include the anteroposterior axis. The Deuterostomia (the Hemichordata, Echinodermata and Chordata) evolved within the Bilateria by producing the mouth as a secondary perforation. Within the deuterostomes the echinoderms and chordates constitute a monophyletic group named Dexiothetica. Hemichordates retain the primitive bilaterian sagittal plane. The Dexiothetica derive from an ancestor like the present-day hemichordate Cephalodiscus which had lain down on the primitive right side (dexiothetism) and acquired a calcite skeleton. The echinoderms evolved from this ancestor by losing the ancestral locomotory tail and gill slit, becoming static, moving the mouth to the centre of the new upper surface and developing radial pentameral symmetry. The chordates evolved from the same ancestor by developing a notochord in the tail, losing the water vascular system, evolving a filter-feeding pharynx and developing a new vertical plane of bilateral symmetry perpendicular to the old bilaterian plane. Evidence derived from certain bizarre Palaeozoic marine fossils (calcichordates) gives a detailed history of the early evolution of echinoderms and chordates and shows how the new bilateral symmetry was gradually acquired in chordates. This symmetry began in the tail (which contained the notochord and was also the leading end in locomotion) and advanced forward into the head.