What shared characteristic does fungi and animals have?

One is that they are both heterotrophs, meaning that they do not make their own energy so therefore have to absorb it from the outside.
Another is that they belong in the “Unikonta” and even more specific they are opisthokonts, meaning that cells who are flagellated, mainly gametes, have only 1 flagellum at the posterior end of the cell (in most cases)

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