Questions & Answers about La dama abrió la puerta.
Because both nouns are singular feminine.
In Spanish, the definite article agrees with the noun in gender and number:
- la dama = the lady
- la puerta = the door
If the noun were masculine singular, you would usually use el. If it were feminine plural, you would use las.
It is perfectly understandable, but in modern everyday Spanish in Spain, dama can sound a bit formal, refined, literary, or old-fashioned, depending on context.
More everyday possibilities are:
- mujer = woman
- señora = lady / madam / adult woman, often polite
So La dama abrió la puerta is grammatically fine, but the choice of dama gives the sentence a slightly elegant tone.