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# Which statement proves that parallelogram KLMN is a rhombus? A. The midpoint of both diagonals is (4, 4). B. The length of KM is √72 and the length of NL is √8. C. The slopes of LM and KN are both 1/2 and NK = ML = √20 . D. The slope of KM is 1 and the slope of NL is –1. Download png

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Answer: D is the correct answer.The slope of KM is 1 and the slope of the NL is -1. Step-by-step explanation:A rhombus is a parallelogram whose sides are equal. Its diagonals perpendicularly bisect each other. that is to say, the product of their slope should be -1.[∵if a line is perpendicular to the other lines, then the product of their slope should be -1.]In the diagram of the Slope of KM=Slope of NL=Product of the inclination of the diagonals=1×-1=-1∴the diagonal of the parallelogram given perpendicularly bisect each other.Therefore,it is a rhombus.