Is the word construiu the same in Brazilian and European Portuguese?

Yes

The word "construiu" is identical in spelling, grammar, and meaning in both Brazilian and European Portuguese. The only differences lie in pronunciation. In Brazilian Portuguese, the vowels tend to be more open and clearly articulated. In European Portuguese, vowels that are unstressed are often "reduced" or shortened, making the word sound more clipped and less melodic to a Brazilian ear.

Brazilian Portuguese Examples

1. Ele construiu uma casa de praia. (He built a beach house.)
2. A empresa construiu um prédio enorme. (The company built a huge building.)
3. Ela construiu uma carreira brilhante. (She built a brilliant career.)
4. O governo construiu uma ponte nova. (The government built a new bridge.)
5. O marceneiro construiu uma mesa. (The carpenter built a table.)

European Portuguese Examples

1. Ele construiu uma moradia de praia. (He built a beach house/villa.)
2. A empresa construiu um edifício enorme. (The company built a huge building.)
3. Ela construiu uma carreira brilhante. (She built a brilliant career.)
4. O Estado construiu uma ponte nova. (The State built a new bridge.)
5. O carpinteiro construiu uma mesa. (The carpenter built a table.)