The taxonomical hierarchy runs like this:
Kingdom Animalia
Phylum Chordata
Class Mammalia
Order Primates
Family Hominidae
Genus Homo
Species Sapiens
If you define "Ape" to be any member of the family Hominidae (the "Great Apes") then chimpanzees, bonobos, gorillas, humans and orangutans all fall within that definition. If you choose the broader definition of any member of the superfamily Hominoidea, which would include the family Hylobatidae (the "lesser apes") then the gibbons come into that definition as well. But if you define Ape as any member of one of these families that is not a member of the genus Homo, then the definition excludes our species, as well as our extinct precursor species.
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--James