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APPRECIATE, VALUE, PRIZE, TREASURE, CHERISH mean to hold in high estimation.

APPRECIATE often connotes sufficient understanding to enjoy or admire a thing's excellence.

e.g. appreciates fine wine

VALUE implies rating a thing highly for its intrinsic worth.

e.g. values our friendship

PRIZE implies taking a deep pride in something one possesses.

e.g. Americans prize their freedom

TREASURE emphasizes jealously safeguarding something considered precious.

e.g. a treasured memento

CHERISH implies a special love and care for something.

e.g. cherishes her children above all

verb with object

protect and care for (someone) lovingly:

〈権利･信念など〉を持ち［守り］続ける

e.g. he cared for me beyond measure and cherished me in his heart.

hold (something) dear:

〈人･動植物など〉をかわいがる, 大切にする, (愛情をこめて)世話をする, 育てる (!進行形にしない)

e.g. I cherish the letters she wrote

e.g. (as adjective cherished) : cherished possessions.

keep (a hope or ambition) in one's mind:

〈希望･感情･考えなど〉を心に抱く; 〈思い出など〉を胸にしまっておく

e.g. he had long cherished a secret fantasy about his future.

Middle English (in the sense ‘treat with affection’): from Old French cheriss-, lengthened stem of cherir, from cher ‘dear’, from Latin carus.