Symmetry Allowed Definition:

A reaction that obeys conservation of orbital symmetry.

Symmetry Allowed Explained:

The phases must be symmetric, this requirement, called conservation of orbital symmetry. In the Diels- Alder reaction, because orbital symmetry is indeed conserved, and the reaction is therefore called a symmetry-allowed process. This reaction is also a cycloaddition. Specifically, it is called a [2+2] cycloaddition, because it involves two different p systems, each of which is associated with two atoms.