In the sentence "The girl is fishing on the lake" would on be a noun and "Fish swim up the river near the lake" would up and near be a noun?
"Girl" and "lake" are nouns in the first sentence.
"Fish" "river" and "lake" are nouns in the second sentence.
Shaniquaa is correct.
The words "on," "up," and "near" are prepositions.
http://www.uottawa.ca/academic/arts/writcent/hypergrammar/partsp.html
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In the sentence "The girl is fishing on the lake," the word "on" is not a noun. Rather, it is a preposition. Prepositions show relationships between other words in a sentence. In this case, "on" shows the relationship between "fishing" and "lake" and indicates the location where the girl is fishing.
Similarly, in the sentence "Fish swim up the river near the lake," both "up" and "near" are not nouns. They are also prepositions. "Up" shows the direction of the fish's movement, while "near" indicates the proximity of the river to the lake.
To identify a preposition, you can think about the function it serves in the sentence. Prepositions often indicate time, location, direction, or manner. They are typically followed by a noun or pronoun, but not always. In these sentences, "on" and "near" are followed by nouns ("lake" and "river" respectively), but "up" is not immediately followed by a noun. Instead, it is followed by an article ("the") and a noun ("river").
Remember, prepositions are not nouns themselves, but rather words that help establish relationships between other words in a sentence.