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Dugesiashows
A) Transverse binary fission
B) Longitudinal binary fission
C) Oblique binary fission
D) No binary fission

Answer
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Hint:Fission is a method of asexual reproduction. Asexual reproduction is a type of reproduction where only single parent gives rises to offspring. There is no involvement of opposite sexes in this type of reproduction.

Complete answer:
Transverse binary fission
It is a mode of asexual reproduction. In transverse binary fission, the cytoplasm separates transversely.This division divides single parents into two equal halves. Example- in ciliated protozoans like Paramecium.
Longitudinal binary fission
In longitudinal binary fission the cytoplasm separates along the longitudinal axis forming two daughter cells. Example- in flagellates like Euglena.
Oblique binary fission
In oblique binary fission the cytoplasm separates obliquely. Example- Ceratium.

Type of division in Dugesia:-
>Dugesia is a genus representing flatworms.
>They are hermaphrodites.
>They reproduce by the means of asexual as well as sexual reproduction reproduction.
>Usually they are reproduced by transverse binary fission.
> Fission occurs when the animals get matured in order to reproduce.
>After attaining maturity, the animal ruptures behind the pharynx.
>Each ruptured part regenerates its missing parts and becomes a new individual.
So, from the above discussion it is clear that Dugesia shows transverse binary fission.

Hence, option A is the correct answer.

Note:Dugesia is a flatworm and we all know that flatworms have regeneration power. So it can regenerate its missing body parts easily and become a full new individual. And one more important thing is that they only reproduce when they attain their maturity.