Question

Why are the filamentous body forms of slime molds (myxomycetes and acrasiomycetes), water molds (oomycetes) and the hyphae of fungi considered a case of convergent evolution?

Answer 1

Convergent evolution is the independent evolution of similar features in species of different lineages.

It creates analogous structures with similar form or function but these structures were not present in the last common ancestor of those groups.  

The filamentous body forms of slime molds, water molds and the hyphae of fungi  is considered a case of convergent evolution because the filaments shape is an adaptation for a nutritional mode as a decomposer.

Answer 2

It is because convergent evolution represents the independent evolution of similar features in species that don't have the same ancestor. In this case filamentous body forms evolved independently, but have the same function: an adaptation for a nutrition of decomposers.