Is a venus fly trap a carnivore, omnivore, or herbivore?

It should be carnivore, since they tend to mostly eat insects and arachnids. It even states it on the wikipedia page, so I'm not sure why you did get it wrong.
Another possible answer is that it isn't any of those since it is a plant, but I'm not sure.

It's classed as a carnivorous plant. Most of its nitrogen is obtained from the flesh of insects,but it obtains other nutrients directly from the soil via its roots,so I suppose,technically,it could be considered an omnivore.

i must say thats an interesting question, technically they would be insectivorous, but if carnivore, omnivore and herbivore were the only answers then carnivore would be correct

if so perhaps your teacher is just trying to be clever because they gain energy from sunlight (which actually makes them a producer and not an omnivore), or maybe because they could accidentally close on plant material instead.

if either of these is the case then please tell your teacher that somebody who knows what they are talking about says carnivore is the right answer.
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oh and sorry DrJ but
"A Carnivore is an organism that derives its energy and nutrient requirements from a diet consisting mainly or exclusively of animal tissue, whether through predation or scavenging"  (Ullrey, D.E. Encyclopedia of Animal Science)

its not limited to animalia but organisms in general
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tell me doctor why would i "read carefully the whole paragraph" of a wikipedia article, i wouldnt trust a wikipedia article as far as i could throw it, i got my information from (wait... can you guess?) the encyclopedia of animal science, which is a reputable enough source in itself.

since youre being so nitpicky about carnivore vs carnivorous, the very wiki page that you spoke of also labels the bengal tiger as "carnivorous"

and you want two online dictionaries? i can go one better
how about two university professors i am friends with, one with an MSc in plant sciences and the other with a PhD in nutrition who to be honest i would trust more than any internet resource you have found.

"and while youre at it" ........... find some similarly qualified individuals that say other wise, if you can.

Sincerely Benjamin BSc MSc Robinson (im not just some kid on the internet so please dont talk to me like one DrJ, thank you)