Answer
$AD||BC$ and $DC||AB$, so it is a parallelogram
(Also see the image and solution below)
Work Step by Step
According to the definition of a parallelogram, opposite sides should be parallel to each other. This means that their slope is the same. So we have to find slopes of opposite sides (See the image above).
The slope of $AD$ must be the same as the slope of $BC$. And the slope of $DC$ must be the same as the slope of $AB$.
In general, we know slope $m=\frac{Δy}{Δx}=\frac{y-y_1}{x-x_1}$ (change in $y$ over change in $x$)
$m_{AD}=\frac{7-1}{-1-1}=\frac{6}{-2}=-3$
$m_{BC}=\frac{10-4}{5-7}=\frac{6}{-2}=-3$
$AD||BC$
$m_{DC}=\frac{10-7}{5-(-1)}=\frac{3}{6}=\frac{1}{2}$
$m_{AB}=\frac{4-1}{7-1}=\frac{3}{6}=\frac{1}{2}$
$DC||AB$
