 This is another coordinate proof. You might want to try it on your own and then come back and watch the video and see if See if you did it right, but we're gonna start at the same way So we're gonna put parallel parallelogram Jack on the graph and the coordinates are on your note sheet And we know that we're given oops, we're given that Jack is a parallelogram. So where it says given we're gonna write Parallelogram Jack and then we're going to put the points on the graph for G for J, AC and K Okay, so now we've got Jack on the graph. We can see that it's Looks like a rectangle and what we're trying to prove is that the opposite sides are congruent And so if we look at the picture, we can see that AC is Opposite of JK. So we're trying to prove that AC is congruent to JK and AJ is Opposite of CK. So we're trying to show that AJ is congruent to CK and just like we did the last proof We're gonna do distance formula to show that these segments are in fact congruent. So I'm gonna start with A and C and Show that hopefully AC the segment AC is equal to the segment JK Now after I use the distance formula for AC I notice that it comes out to a whole number of three and so if I think about it I can look at my picture and see that I have horizontal and vertical lines or segments and so instead of having to do all this work of using the distance formula, I can actually Just count on the graph But because it's a coordinate proof you need to have a way to back up your answer And so that's why we show the distance formula, but we can also look here and see that it's one two three units long But we are gonna use the distance formula just to show that there's actual proof that these segments are congruent So now we're gonna do JK and See if we get three And after doing the distance formula again, we see that sure enough we do get the answer of three So we have now proven that AC and JK are congruent Now I want to do the same work to show that AJ and CK are congruent And after doing the distance formula again for AJ and for CK, we see that AJ is five units and sorry AJ and CK come out to be congruent both equal to five So we have proven that Jack is a parallelogram Because the opposite sides are congruent