Which of the following terms is synonymous with 'lively'?

The term 'vivace' is synonymous with 'lively' because it is an Italian musical term that indicates a fast and spirited tempo. When a piece of music is marked as vivace, it sets an upbeat and energetic mood, encouraging a lively performance. This makes it the most accurate choice among the options presented.

In contrast, 'adagio' refers to a slow tempo, conveying a calm and relaxed feel, while 'moderato' indicates a moderate speed, which is neither fast nor slow. 'Piano' denotes a soft dynamic level, indicating how loudly or softly music should be played, but does not relate to tempo or liveliness. Each of these terms describes different aspects of music, making vivace the clear choice for describing a lively character.