Learn Hardcore German: Die Frau, die im Park tanzt, ist freundlich. - The woman who dances in the park is friendly.

Because it’s a relative clause. In German, all relative clauses are set off by commas, regardless of whether they are restrictive or non‑restrictive. The clause die im Park tanzt modifies die Frau and is inserted into the main clause.

Why is the relative pronoun die and not der or das?

Antecedent: die Frau (feminine singular)
Function in the relative clause: subject (she dances) → nominative
Nominative feminine singular relative pronoun: die
So you get: Die Frau, die im Park tanzt, …

Is the first Die the same word as the second die?

No. They look the same but have different functions:

The first Die is the definite article for Frau. It’s capitalized only because it starts the sentence.
The second die is a relative pronoun referring back to Frau.
They share the same form by coincidence of paradigm, but they’re different parts of speech.

Why does the verb tanzt go at the end of the relative clause?

Relative clauses are subordinate clauses, and German subordinate clauses place the finite verb at the end. Hence: … die im Park tanzt. In standard written German, keep non‑verbal material (like im Park) before the final verb; avoid … die tanzt im Park in careful writing.

Why is it im Park and not in dem Park or in den Park?

im = contraction of in dem (dative).
With location (Wo?), two‑way preposition in takes the dative: im Park.
With direction (Wohin?), it takes the accusative: in den Park (“into the park”).

Why is freundlich not freundliche?

After the verb sein, adjectives are predicative and take no endings: Die Frau ist freundlich.
With an attributive adjective before a noun, you add an ending: die freundliche Frau.

Can I use welche instead of die?

Yes: Die Frau, welche im Park tanzt, ist freundlich. That’s grammatical but sounds more formal/literary. In everyday German, die is more common.

How do I choose the case of the relative pronoun?

By its role inside the relative clause (not by the case of the noun it refers to):

Subject: die (Nom.) → die im Park tanzt.
Direct object: die (Acc.) → die ich im Park sehe (“whom I see”).
Object of a preposition: der (Dat.) → mit der ich im Park tanze (“with whom I dance”).
Possession: deren (Gen.) → deren Musik ich höre (“whose music I listen to”).

Can I omit the relative pronoun like English sometimes does?

No. German does not allow dropping the relative pronoun.
Ungrammatical: Die Frau, ich im Park sehe, …
Correct: Die Frau, die ich im Park sehe, …

Can I use wer here instead of die?

No. wer introduces “headless” relatives meaning “who(ever).” It doesn’t refer back to a specific noun.
Example of wer: Wer im Park tanzt, ist freundlich (“Whoever dances in the park is friendly”).

Could I put the relative clause at the very end: Die Frau ist freundlich, die im Park tanzt?

Not in standard German. A relative clause should directly follow its antecedent (Die Frau). The end‑position version is only used as a spoken afterthought and is considered incorrect in careful writing.

Is tanzt the correct verb form?

Yes. The relative pronoun die stands for “she,” so the verb is 3rd person singular: tanzt.
Compare plural: Die Frauen, die im Park tanzen, sind freundlich.

Do the commas change where ist appears?

They mark the insertion of the relative clause but don’t change main‑clause word order. The main clause is still verb‑second: Die Frau ist freundlich. The relative clause is simply inserted after Die Frau: Die Frau, die im Park tanzt, ist freundlich.

Can I rewrite it with a participle instead of a relative clause?

Yes: Die im Park tanzende Frau ist freundlich. This participial construction is concise and common in written German; it’s equivalent in meaning to the relative clause version.