Question

Need proof that ABCD is a parallelogram

Answer 1

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\\(5-3)/(6-1) =2/5\\BOTTOM\\(-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:
`√(29)`

BOTTOM:
`√(29)`

RIGHT:
`√(17)`

LEFT:
`√(17)`

As the lengths are the same, the sides are congruent