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?

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.

the backbone of the dna and rna compound is sugar phosphate.