Neither "protozoa" or "algae" are clearly defined groups like "Animals," or "mammals." Both groups are very diverse. Euglena are classified as "flagellates," and the flagellates are normally considered protozoans. Most people also consider Euglena to be a species of algae.
Lets assume that you are talking about those algae that are in the protist kingdom.
Then here are some similarities:
1) They have nuclei, and can reproduce by mitosis followed by cell division.
2) Many in both groups are able to move.
3) Like protozoans, some algae, such as the Euglena, are able to eat food.
4) Like the algae, some protozoans, like Paramecium bursia, are able to do photosynthesis.
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