Question

Which statement proves that parallelogram KLMN is a rhombus?

Answer 1

Answer: 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=$\frac{7-1}{7-1}=\frac{6}{6}=1$

Slope of NL=$\frac{5-3}{3-5}=\frac{2}{-2}=-1$

Product of slope of diagonals=1×-1=-1

∴diagonals of given parallelogram perpendicularly bisect each other.

Therefore,it is a rhombus.

Answer 2

The real answer is D lol.