* Animal-like protists do not have chlorophyll: This is correct. They cannot produce their own food through photosynthesis like plants and algae do. Instead, they obtain nutrition by consuming other organisms.
* Animal-like protists are called protozoans: This is also correct. "Protozoa" is a broad term for single-celled eukaryotic organisms that are not plants, fungi, or animals.
* Protozoa meaning "first animals" is misleading: While the name "protozoa" implies a connection to animals, protozoans are not directly ancestral to animals. They share a common ancestor with animals, but diverged into separate evolutionary lineages a long time ago.
Therefore, it's better to say:
* Animal-like protists, also known as protozoans, are single-celled eukaryotes that lack chlorophyll and obtain nutrition by consuming other organisms. They are not directly related to animals, but they share a common ancestor with them.