34.0k views
2 votes
Need proof that ABCD is a parallelogram

Need proof that ABCD is a parallelogram-example-1
User NeoVe
by
6.7k points

1 Answer

2 votes

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

Need proof that ABCD is a parallelogram-example-1
User Gameveloster
by
6.7k points