Green algae is considered an ancestor of modern plants because

I think they have the same photosynthetic pigments because green algae and plants cells have the same kind of chlorophyl, they have similar wall cells, both make their own food during photosynthesis etc ...

The answer to your question A link between green algae and land plants has been clear to biologists for. The remainder of Chlorophyta constitutes a monophyletic group. This major bifurcation in green plant evolution implies a single common ancestor to the two lineages, but, of green algal phylogeny, which is reflected in modern classification.