Чьему дедушке принадлежит статуэтка, которую мы оцениваем?

Questions & Answers about Чьему дедушке принадлежит статуэтка, которую мы оцениваем?

Why is the sentence using чьему дедушке instead of the Nominative чей дедушка?
The verb принадлежит (belongs) requires the owner to be in the Dative case, because something belongs to them. Therefore, дедушка becomes дедушке, and the question word чей (whose) must match its case, gender, and number, becoming the Dative masculine чьему.
Дедушка ends in -а and declines like a feminine noun. Why does чей use the masculine ending чьему instead of a feminine one?
Even though дедушка declines like a feminine noun, its actual gender is masculine because it refers to a male person. Modifiers like adjectives and pronouns always match the true gender of the noun. So, we use the masculine Dative чьему alongside the feminine-looking дедушке.
Why is которую in the Accusative case if it refers to статуэтка, which is in the Nominative case?
The relative pronoun который takes its gender and number from the noun it refers back to (the feminine singular статуэтка), but its case comes from its grammatical role in its own clause. In the second part of the sentence, we are appraising the statuette. Since it is the direct object of оцениваем, it must be in the Accusative case: которую.
Is оцениваем an imperfective or perfective verb here?
It is imperfective. Оценивать means to appraise or to evaluate as an ongoing action, which matches the English 'are appraising'. Its perfective pair is оценить, which would imply the appraisal has been completed.

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