Why are physical properties such as hardness or cleavage useful to geologists when identify minerals?

Physical properties are controlled by the mineral's chemical composition and atomic structure, this combination is distinct in each mineral.

Explanation:

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Since the physical properties depend on the mineral's chemical composition and the atomic structure (molecular arrangement), we can distinguish different minerals by measuring out hardness, cleavage and other properties in order to analyze their behavior under several conditions and subsequently  use them in a particular application.

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