Is a cucumber considered a green vegetable?

Yes, it is vegetable. It can be eat raw, but it belongs to vegetable, not fruit.

Vegetable means an edible plant or part of a plant, but usually excludes seeds and most sweet fruit. This typically means the leaf, stem, or root of a plant. In broad terms, a fruitis a structure of a plant that contains its seeds (comes from the flower).

So, although we treat cucumbers as vegetables (put them in salads, on Sandwiches, etc), they are technically fruit.