Every sentence in this lesson puts the noun in the nominative case — the subject of the sentence, or a predicate noun after sein ("to be"). Unlike the indefinite article ein/eine, the definite article "the" doesn't just track gender — it inflects for all four cases, and (unlike ein) it also has a plural form. In the nominative:

This is the base/dictionary form of the definite article — the citation form you'll see in a dictionary (der Hund, die Katze, das Handy). It changes in the other cases: den/die/das/die in the accusative, dem/der/dem/den in the dative, des/der/des/der in the genitive.