Breakdown of Ты ответил верно.
ты
you (singular)
ответить
to answer (perfective)
верно
correctly; that is right
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Questions & Answers about Ты ответил верно.
Why use верно here instead of правильно?
Both mean 'correctly' and are highly interchangeable in this context. Правильно literally means 'according to the rules' (from правило - rule), while верно relates more to truth or being faithful to the facts (from вера - faith or belief). You can safely use either!
Why is the perfective verb ответил used here?
Ответил focuses on the result of a single, successfully completed action: you gave an answer, and it was right. If you used the imperfective отвечал, it would focus on the process ('you were answering') or a repeated habit ('you usually answered correctly').
How would we apply this lesson's grammar to say 'You answered SO correctly THAT...'?
Because верно is an adverb, you must use так (so) rather than такой (such). You would say: Ты ответил так верно, что... You only use такой when modifying a noun, like in такой верный ответ (such a correct answer).