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.

D is  the right answer.The slope of KM is 1 and the slope of NL is –1.

Step-by-step explanation:

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

i.e. product of its slope should be -1.

[∵if one line is perpendicular to the other lines then product of its slope should be -1.]

In diagram

Slope of  KM=

Slope of NL=

Product of slope of diagonals=1×-1=-1

∴diagonals of given parallelogram perpendicularly bisect each other.

Therefore,it is a rhombus.

a

step-by-step explanation: