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Which statement proves that parallelogram KLMN is a rhombus? The midpoint of both diagonals is (4, 4). The length of KM is StartRoot 72 EndRoot and the length of NL is StartRoot 8 EndRoot. The slopes of LM and KN are both One-half and NK = ML = StartRoot 20 EndRoot. The slope of KM is 1 and the slope of NL is –1.

Sagot :

The correct statement proves that parallelogram KLMN is a rhombus.

The slope of KM is 1 and the slope of NL is –1.

What is the rhombus?

A rhombus is a parallelogram whose all sides are equal. Its diagonals perpendicularly bisect each other.

If one line is perpendicular to the other lines then the product of its slope should be -1.

The slope of the KM is;

[tex]\rm Slope = \dfrac{7-1}{7-1}\\\\Slope=\dfrac{6}{6}\\\\Slope=1[/tex]

The slope of the KM is 1.

And the slope of NL is;

[tex]\rm Slope =\dfrac{5-3}{3-5}\\\\Slope=\dfrac{2}{-2}\\\\Slope=-1[/tex]

The slope of NL is -1.

Hence, The slope of KM is 1 and the slope of NL is –1.

To know more about Rhombus click the link given below.

https://brainly.com/question/26078375

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Answer:

The correct statement proves that parallelogram KLMN is a rhombus.

The slope of KM is 1 and the slope of NL is –1.

Step-by-step explanation:

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