Question

Need proof that ABCD is a parallelogram

Answer 1

Step-by-step explanation:

To prove that two sides are parallel on a graph, we must show that their slopes are the same. Plotting this on Desmos, we get the first image attached.  Finding the slopes of each line, we get

$TOP\\\frac{5-3}{6-1} =2/5\\BOTTOM\\\frac{-1-(-1)}{7-2} =2/5\\RIGHT\\-4\\LEFT\\-4$

As the top slope is the same as the bottom, and the right is the same as the left, this is a parallelogram.

To prove that two sides are congruent, we must find their lengths. The distance formula is

$\sqrt(x_{1}+x_{2})^2+(y_{1}+y_{2})^2 }$

Finding the distances, we get

TOP: $\sqrt{29}$

BOTTOM: $\sqrt{29}$

RIGHT:$\sqrt{17}$

LEFT:$\sqrt{17}$

As the lengths are the same, the sides are congruent