Which aquatic plant has reddish-brown stems that are leafy, with flat leaves arranged oppositely or in whorls of three?

The correct choice, Southern naiad, is characterized by its distinctive reddish-brown stems that are leafy. This aquatic plant typically exhibits flat leaves that are arranged either oppositely or in whorls of three, which helps to easily identify it in its natural habitat. The arrangement of the leaves is particularly noteworthy, as it distinguishes Southern naiad from other aquatic plants that may have different leaf structures or arrangements.

Sago pondweed, while a common aquatic plant, does not possess the reddish-brown stems or the specific leaf arrangements described in the question. Instead, it features long, narrow leaves that are more elongated and are not typically whorled or oppositely arranged. Coontail is another aquatic plant, but it has a very different form; it is characterized by its whorled, bushy appearance with distinctly divided leaves, which do not match the description provided. Lastly, filamentous algae do not have stems or leaves at all, as they are composed of long, thread-like structures that form mats in water bodies, separating them clearly from the plant characteristics described in the question.

Thus, Southern naiad is the only option that aligns with the outlined physical traits, making it the accurate choice.