Learn Hardcore German: Der Lehrer antwortet dem Schüler geduldig. - The teacher answers the student patiently.

The verb antworten in German always takes a dative object to indicate the person being answered. Since der Schüler is masculine singular in the dative, it changes to dem Schüler.

Why is there no direct (accusative) object in this sentence?

Because antworten is an intransitive verb that governs the dative. It doesn’t need (and can’t take) an accusative object—only the person you answer (dative) is needed.

Why does geduldig appear at the end of the sentence?

German follows a loose order for adverbs: Time – Manner – Place (TMP). Here there’s no time or place adverb, so the manner adverb geduldig (“patiently”) comes after the object, placing it at the end.

Is geduldig an adjective or an adverb here, and why is it uninflected?

It’s an adjective used adverbially. In German, when you use an adjective to describe how something is done (manner adverb), you don’t add endings—it stays in its base form, geduldig.

How do you conjugate antworten in the present tense for “he answers”?

“Er antwortet” is the third-person-singular form. The full present-tense conjugation is: ich antworte
du antwortest
er/sie/es antwortet
wir antworten
ihr antwortet
sie/Sie antworten

What’s the difference between antworten and beantworten?

antworten is intransitive and takes a dative object (jemandem antworten).
beantworten is transitive and takes an accusative object (etwas beantworten).
Example: – Ich antworte dir. (dative)
– Ich beantworte die Frage. (accusative)

Can you also say “Er antwortet auf die Frage” instead of using a dative?

Yes. If you want to answer a thing rather than a person, you can say antworten auf + accusative: – Er antwortet auf die Frage.
That construction shifts the “what” to an accusative object with auf.

Could I rephrase the sentence with the same meaning, for example using eine Antwort geben?

Absolutely. You can turn it into a different verb + noun: – Der Lehrer gibt dem Schüler geduldig eine Antwort.
This uses geben (to give) with eine Antwort (an answer) and keeps the dative dem Schüler.