Answer
None
Work Step by Step
Our aim is to apply the distance formula to compute the type of triangle that is given in the picture.
The distance formula is given by the following formula:
$d = \sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2}$
We will compute the lengths of one pair of opposite sides of the parallelogram.
$GH= \sqrt {(0-6)^2 + (0-0)^2}=6$ and $IJ= \sqrt {(9-3)^2 + (1-1)^2}=6$ and $HI= \sqrt {(6-9)^2 + (0-1)^2}=\sqrt {10}$and $GJ= \sqrt {(0-3)^2 + (0-1)^2}=\sqrt {10}$
We can see that the lengths of one pair of opposite sides of the parallelogram are not having equal lengths, this means that they are not congruent.
Next, we will compute slope of two consecutive sides of the parallelogram.
$m\overline{GH}= \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-0}{6-0}=0$ and $m\overline{HI}= \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-0}{9-6}=\dfrac{1}{3}$
We can see that the slopes of the consecutive sides of the parallelogram are not having equal lengths, this means that they are not congruent.
Therefore, the given parallelogram is neither a square and not a rhombus.
