Mater gaudet, quia filia salva domum rediit.

Mater is in the nominative singular, which is the case used for the subject of the verb. In this sentence, mater is the one who rejoices, so it has to be nominative.

Its dictionary form is mater, matris (mother), a third-declension noun. The form matrem would be accusative singular, which would usually mark a direct object, not the subject.

Because the subject is mater = she / the mother, the verb must be third person singular.

• gaudeo = I rejoice / I am glad
• gaudes = you rejoice
• gaudet = he/she/it rejoices

So mater gaudet means the mother rejoices.

Quia means because and introduces a subordinate clause giving the reason for the main statement.

So the sentence is structured like this:

• main clause: Mater gaudet
• reason clause: quia filia salva domum rediit

In other words, the mother rejoices because something happened: her daughter returned home safe.

Because filia is the subject of the verb rediit in the quia clause.

So there are really two separate subject-verb pairs in the sentence:

• mater gaudet
• filia rediit

Even though the second clause depends on quia, it still has its own subject, and that subject must be in the nominative.

Because salva agrees with filia, not with domum.

Salva is an adjective meaning safe. Here it is used predicatively, describing the condition of the daughter when she returned. Since filia is:

• feminine
• singular
• nominative

the adjective must match it:

• filia salva

If it were salvam, that would be accusative feminine singular, which would not fit filia here.

It is still an adjective, not an adverb.

Latin often uses an adjective with the subject to express a state or condition:

• filia salva rediit = the daughter returned safe

English sometimes uses an adjective similarly, as in She came back safe. So salva describes filia, not the manner of the action in the way an adverb would.

Because Latin often uses the accusative without a preposition to express motion toward home.

So:

• domum = homeward / to home / home

This is a special and very common idiom. With ordinary nouns for places, Latin often uses a preposition such as ad or in, but domus has some special forms and uses.

For example:

• domum venit = he came home
• domi manet = he stays at home

Rediit is perfect tense, meaning returned or has returned.

The mother is glad because the daughter’s return has already happened. So the sequence makes sense:

• Mater gaudet = the mother is glad now
• quia filia salva domum rediit = because the daughter came back safely / has returned home safe

The verb comes from redeo, redire, redii/redivi = to go back, return.

Rediit specifically means went back or returned.

• iit = went
• venit = came
• rediit = came back / returned

So rediit adds the idea of coming back to a place where the daughter belonged or was expected. That is why it fits naturally with domum.

Yes. Latin word order is much more flexible than English word order because the endings show the grammatical roles.

For example, these would still mean essentially the same thing:

• Mater gaudet, quia filia salva domum rediit.
• Quia filia salva domum rediit, mater gaudet.
• Filia salva domum rediit, quia mater gaudet. — this one changes the logic, so not the same
• Mater, quia filia domum salva rediit, gaudet. — possible, though less natural

The original order is clear and natural. It presents the main idea first, then the reason.

Yes. In this sentence, quia introduces a reason that the speaker presents as a fact, so the indicative is normal:

• filia salva domum rediit

That is a straightforward statement: the daughter returned home safe. Latin commonly uses the indicative after quia when the cause is treated as real or factual.

Yes. Learners often notice the double i.

The verb is from redeo. In the perfect, one common form is rediit:

• re-
  • iit -> rediit

You may also see related perfect forms such as rediit and forms built on redii. The important thing for a beginner is simply to recognize rediit as he/she returned.