Bilaterally symmetrical and acoelomate animals are exemplified by

Coelom: The body cavity; which is lined by mesoderm is called coelom. 

Coelomates: If coelom is present, the animal is called coelomate, e.g. Annelids, Molluscs, Arthropods, Echinoderms, Hemichordates and Chordates. 

Pseudoceolomates: If the body cavity is not lined by mesoderm, but the mesoderm is present as scattered pouches in between the ectoderm and endoderm, the animal is called pseudocoelomate, e.g. Aschelminthes. 
Acoelomates: When the body cavity is absent, the animal is called acoelomate, e.g. Platyhelminthes.

SYMMETRY:

Some animals are almost asymmetrical. Their body cannot be divided into two equal halves from any plane, e.g. sponges. 

Radial Symmetry: In the case of radial symmetry, any plane passing through the central axis divides the body into two identical halves, e.g. Coelenterates, Ctenophores, Echinoderms, etc. 

Bilateral Symmetry: In the case of bilateral symmetry, the body can be divided into two identical halves only through a single plane, e.g. Platyhelminthes, Annelida, Arthropoda, etc.