 This problem is not on your note sheet, but it is important to know how to do for your assignment. So I'm going to show you, it's kind of like a coordinate proof, but what it asks you is to identify if A, B, C, D is a trapezoid. After you've done that, it then asks to identify whether or not it's an isosceles trapezoid. So what we know about a trapezoid is that one pair of opposite sides has to be parallel. Well, in order to prove segments are parallel, we need to show that they have the same slope. So the way that you're going to do this problem, or the way that you're going to start it, is you're going to find the slope for every single combination of A, B, C, C, D, and A, D. So you're actually going to do the slope formula four times. So what we're going to do is we're going to find the slope of A, B. And again, we're just using the slope formula. So 8 minus a negative is going to be plus 4, and 0 minus a negative is going to be plus 8. And I'm just using the points A and B. So that gives me 12 over 8, and that reduces, 4 goes into 12 three times, 4 goes into 8 twice. So the slope of A, B is 3 over 2. Next I'm going to do the slope of B, C. So if you want to pause for a minute and go ahead and calculate the slope of B, C, and then come back and check to see if you get the answer right. I'm going to pause the video and fill in the rest of the slope formula. Okay, so the slope of B, C you should have gotten 0. Now I'm going to do the same thing for C, D and for A, D. Again, I'm going to pause the video and do the work of finding the slope for C, D and A, D. You can go ahead and do the same on your paper. Okay, so now what we're looking at is these four slopes. I have a slope of 3 over 2, a slope of 0, a slope of 3 over 2, and a slope of negative 3. Remember, all we need to have a trapezoid is one pair of opposite sides being parallel. And sure enough, we see right here we have 3 over 2 and right here we have 3 over 2. So it is a trapezoid because A, B is parallel to C, D. Now by the way, I didn't draw this on a graph. That might help you. It's really nice to be able to visualize these things. I didn't have a graph to draw on for this video, but of course if you were doing your assignment or a quiz or a test, definitely I would suggest that you plot these points so that you're actually looking at the picture because that's going to hopefully help you. Okay, so this is a trapezoid because A, B is parallel to C, D. So we have one pair of opposite sides parallel. Now let's move to this question or this part of the problem where it says identify if it's isosceles or not. So remember that in order to have an isosceles trapezoid, the legs have to be congruent. Now remember that the legs are the non-parallel sides of the trapezoid. So that means I have to show that B, C is congruent to A, D because those are the legs. They're the non-parallel sides. Again, if you draw a picture that might help you see that. But again, if you can remember that the legs are the non-parallel sides, you can figure it out that way. So how do I show that two segments are congruent? Well, I have to show that they're the same length. So now I'm going to switch gears and I'm going to move my screen down here a little bit and what we're going to do is we're going to use the distance formula to show whether or not B, C is congruent to A, D. So I'm just going to go to the next screen to finish this proof to see if this is isosceles or not. So here we have our points B, C and A, D and what we want to figure out is B, C congruent to A, D because if it is, then we know we have an isosceles trapezoid. So we're just going to go ahead and do the distance formula. So using B and C, go ahead, plug the numbers in to the distance formula and see what you get. I'm going to pause the video and fill in the values. So hopefully you got an answer of 6 for B, C. 6 minus 0 squared is 36. 8 minus 8 squared is 0. So you get the square root of 36, which is 6. Now go ahead and do the same thing for A, D. So when you put in the values for A, D, you can see what happens here is we get negative 6 plus 8 squared and negative 10 plus 4 squared. When we add that together, 4 plus 36, we get 40, the square root of 40. Well clearly, 6 and square root of 40 are not equal. So that means that B, C does not equal A, D. So therefore, and these little dots when they're in the form of a triangle, I just messed it up, I mean therefore. So therefore, this figure A, B, C, D is a trapezoid because we saw that we had one pair of parallel sides, but it's not isosceles. Hopefully that helps you on the problems that are on your assignment.