Learn Arabic (Modern Standard): الباب مفتوح.

In Arabic, present-tense words for "is" or "are" are simply left out. You create a complete sentence just by placing the noun (الباب) right next to the adjective giving information about it (مفتوح). This type of phrase is called a nominal sentence.

Why doesn't مفتوح have ال (the) at the beginning like الباب does?

This is the secret to making a sentence instead of just a phrase! The subject (الباب) is definite and has ال (the). The predicate adjective (مفتوح) is indefinite, meaning it does not have ال. If both had ال, it would just mean "the open door" instead of the full sentence "the door is open."

Why is the word مفتوح in its masculine form here?

In a nominal sentence, the adjective giving information about the noun still has to match that noun's gender. Since الباب (the door) is a masculine noun, مفتوح remains in its default masculine form. If we were talking about a feminine noun like a window, we would use the feminine form of the adjective.

Are the words مفتوح (open) and مفتاح (key) related?

Yes, they share the same three core root letters. In Arabic, words built from the same root have related meanings. This root is all about opening, so مفتوح means "open" and مفتاح is the tool you use to open things!