Historical question on "open"

[Rudolph C Troike]

        A visiting scholar from Korea today wondered why we use
"open" rather than "opened" in a sentence such as the following:

        The door is open.
        The door is closed.

whereas we use the past participle "closed" in the parallel sentence.
German and Spanish both use past participles (geo:ffnet, abierto).
Does anyone happen to know the story of how we came to have just "open"
in this context?

        Rudy