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

Yes

The word provar is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. It retains the same core functions: to taste (food), to prove (a fact), and to try on (clothing). The differences are limited to:

• Pronunciation: In Continental Portuguese, unstressed vowels are often more closed or "reduced" (sometimes sounding almost silent), whereas in Brazilian Portuguese, vowels tend to be more open and clearly articulated. Additionally, the pronunciation of the final "r" varies significantly between the two dialects.
• Contextual Syntax: While the word "provar" itself does not change, the way a speaker refers to objects near them often does. A Brazilian speaker is more likely to use the demonstrative esse (that) in casual conversation, whereas a Portuguese speaker adheres more strictly to este (this) for objects within immediate reach.

Brazilian Portuguese Examples

1. Eu quero provar esse bolo. (I want to taste this cake.)
2. Ele provou que o réu é inocente. (He proved that the defendant is innocent.)
3. Você pode provar essa blusa? (Can you try on this blouse?)
4. A gente vai provar esse novo método. (We are going to test this new method.)
5. Ela provou a comida e achou salgada. (She tasted the food and thought it was salty.)

European Portuguese Examples

1. Eu quero provar este bolo. (I want to taste this cake.)
2. Ele provou que o arguido é inocente. (He proved that the defendant is innocent.)
3. Podes provar esta blusa? (Can you try on this blouse?)
4. Nós vamos provar este novo método. (We are going to test this new method.)
5. Ela provou a comida e achou salgada. (She tasted the food and thought it was salty.)