Question 408015
Using a coordinate geometry proof, which method below is a correct way to prove a quadrilateral is a rhombus?
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1.  Opposite sides have congruent slopes.
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No, for that is true of any parallelogram
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2.  The diagonals have the same midpoint, and one pair of opposite sides have equal lengths.
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No, for that's true not only of all parallelograms, but isosceles trapezoids
as well.
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3.  The diagonals have the same length.
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No, for that's true of all rectangles and isosceles trapezoids. 
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4.  The diagonals have the same midpoint and two adjacent sides have the same length.
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Yes, that's true only for rhombuses.

So 4 is the correct choice.

Edwin</pre>