active、energetic、vigorous、brisk与lively这些形容词均有“积极的、活跃的”之意。
active ：指有活动能力，强调与消极或休止相反的积极活动状态。
Although he's nearly 80, he is still very active.尽管快80岁了，他还是十分活跃。
energetic ：提精力充沛、奋力从事某事业。
He knew I was energetic and dynamic and would get things done.他知道我精力充沛、生气勃勃，会把事情办成的。
vigorous ：指不仅表现积极、有生气，而且固有精力和活力十分旺盛。
a vigorous campaign against tax fraud坚决打击骗税的运动 Take vigorous exercise for several hours a week.
每周做几个小时剧烈运动。
brisk ：指动作敏捷、充满活力、轻快活泼地从事某项工作或活动。
a brisk walk轻盈的步履 to set off at a brisk pace
以轻快的步伐上路 年轻美貌的妻子发现自己竟被一个活泼丑陋的女人取而代之。
The pretty young wife finds herself having been supplanted by a brisk, unlovely woman.
lively ：侧重指轻快、机智、有生气。
an intelligent and lively young woman聪慧而充满活力的年轻女士 Josiah Davis, the director, coaxes lively and lucid performances from all the actors.
导演乔赛亚·戴维斯连哄带劝地使所有演员进行生动而清晰的表演。
——《纽约时报》同义词辨析
