Answer:
yes, parallelogram ABCD is a square.
Step-by-step explanation:
Given information: ABCD is parallelogram with vertices A(0,4), B(2, 2), C(4,4), and D(2,6).
We need to check whether this parallelogram is a square or not.
The opposite side of a parallelogram are parallel and congruent. If the interior angles a parallelogram are right angles then the parallelogram is square.
Formula for slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Now, find the slopes of each side.
[tex]m_{AB}=\dfrac{2-4}{2-0}=-1[/tex]
[tex]m_{BC}=\dfrac{4-2}{4-2}=1[/tex]
[tex]m_{CD}=\dfrac{6-4}{2-4}=-1[/tex]
[tex]m_{AD}=\dfrac{6-4}{2-0}=1[/tex]
The product of slopes of two perpendicular line is -1.
The product of slopes of any two consecutive sides is -1. It means all interior angles are right angle.
Therefore, the parallelogram ABCD is a square.
