In isolation, yes. In this exercise, the full prepositional phrase is i dteach an fhir, and in the noun phrase teach an fhir (“the man’s house”, literally “the house of the man”), both teach and fear are definite; this is why i dteach an fhir translates as “in the man’s house” (literally “in the house of the man”).
I once got distracted and gave an answer half in Irish and half in English :-) I've also reported that my answer should be accepted and just after I clicked the button I noticed that I completely selected a nonsensical word like "car" instead of "the". Proofreading is the biggest lesson that duolingo is teaching me XD
ok, so after the preposition "i" is one of the five circumstances in which nouns can be eclipsed
the others being 1) genitive plurals after "na" 2) after possessive pronouns ár, bhur, a 3) in Connaught or Munster dialect, after ag an, ar an, as an, faoin, ón, tríd an 4) after seacht, ocht, naoi agus deag
There are a few other circumstances in which nouns are eclipsed:
- 2a) after dár, faoinár, inár, lenár, ónár, and trínár ;
- 2b) after dá, faoina, ina, lena, óna, and trína when meaning “… their”;
- 2c) after ár dhá, bhur dhá, and a dhá (“their two”) ;
- 3) also allowed in the Caighdeán ;
- 3a) in Connacht, Munster, and the Caighdeán, after chuig an, dar an, leis an, mar an, roimh an, thar an, and um an ;
- 3b) in the Caighdeán, eclipsis is also allowed after den, don, fairis an, and insan / insa / sa ;
- 6) in phrases like ar gcúl, ar ndóigh, ar dtús, go bhfios dom, etc.