Final answer:
The animal groups that show deuterostome development are echinoderms and chordates. Sponges, nematodes, and annelids are not deuterostomes as they are part of other developmental categories like Parazoa or Protostomia.
Step-by-step explanation:
The animal groups that show deuterostome development include echinoderms and chordates. Deuterostome development is characterized by the mouth forming second during embryonic development, with the blastopore becoming the anus. This is in contrast to protostomes, where the mouth forms first. The phyla Echinodermata, which includes sea stars, sea urchins, and sea cucumbers, and Chordata, which includes vertebrates as well as some invertebrate subphyla, exhibit these deuterostome characteristics.
Sponges (Porifera), nematodes (Nematoda), and annelids (Annelida) do not exhibit deuterostome development; these groups are either part of the Parazoa (sponges, which do not have true tissues) or are protostomes. Recall that annelids have well-defined segmentation and are known for their chitinous chaetae, but they are not deuterostomes.