 In this video, parallelogram or not, we are given a figure and we are asked to decide whether it is indeed a parallelogram. This is where we're going to use the six tests for parallelograms that we just talked about. And if the information given to us matches one of those tests, then we can say, yes, it is a parallelogram. So for our first one, we're given two sets of opposite sides that are congruent. If we look at our tests, that's going to be that first theorem that says both pairs of opposite sides are congruent. So we're going to use a parallelogram and we're going to put our answer here in the form of a conditional statement. If both pairs of opposite sides are congruent, then this is a parallelogram. Remember, this is the symbol for parallelogram, this is the symbol for congruent. For number two, we are told that we have one set of opposite angles that are congruent. And if you look at this number three test, it says that we need to know that both pairs of opposite angles are congruent. So this is not going to be a parallelogram. If the answer is no, it asks us in the directions to draw a counter example. So I'm going to draw a quadrilateral that has one set of opposite angles congruent but is clearly not a parallelogram. And this is where the answers can vary, but in my answer here, I have one set of opposite angles that are congruent. But clearly this is not a parallelogram, this is actually a kite. And a lot of the counter examples, because the kite is kind of a unique parallel, or a unique quadrilateral, this is often a good counter example to use. So whenever you have a no, you need to give a counter example and it can be as simple as just drawing a picture that matches that given information but is clearly not a parallelogram. Number three tells us that we have opposite sides parallel. These are the parallel symbols. And the same set of opposite sides are also congruent. And this is that one that number five says a pair of opposite sides is both parallel and congruent at the same time. I'm going to put that yes answer in the form of our if-then conditional statement. If a pair of opposite sides is parallel and congruent, then it is a parallelogram. Number four just tells us that opposite sides are parallel and we know that this is our basic figure for a parallelogram. And this is that first test for a parallelogram, say if both pairs of opposite sides are parallel, then it is a parallelogram. Number five looks similar to our number three question, but this time we have this set of opposite sides parallel and then the separate set of opposite sides are congruent. So this does not meet this test that both or one opposite side is both parallel and congruent. So I want you to take a second, maybe even pause the video and see if you can come up with a counter example where one set of opposite sides is parallel and the other set of opposite sides is congruent that shows it is not a parallelogram. And there are varying answers for what I come up with is a trapezoid. We can say that if these opposite sides are congruent and these opposite sides are parallel, this meets the criteria given to us, but it is clearly not a parallelogram. Remember, whenever you have a no answer, you have to draw a picture for your counter example. Number six gives us information about diagonals and this number four is the only test that talks about diagonals. They must bisect each other. And in this case, they clearly do. Remember bisect means is just cut in half. So we know that this diagonal is cut in half and this diagonal is also cut in half. So we can say yes, this is a parallelogram. If diagonals bisect each other, then it's a parallelogram. Number seven gives us information about three angles but not the fourth angle. We don't know what this is. But remember, if it's any four-sided figure, a quadrilateral will always add up to 360 degrees. So I can find that fourth angle by subtracting the other three angles 65 plus 115 plus 65 equals 245. When I do that, I know that last angle is going to be 115 degrees also. We're going to look at consecutive angles being supplementary because when I put that in, I know these are consecutive angles that adds up to 180 degrees and these are consecutive angles that add up to 180 degrees. In fact, all the way around, you show that the consecutive angles are supplementary. So we can say yes, this is a parallelogram because of this number six test. If all consecutive angles are supplementary, then it's a parallelogram. We also could say, because we know that this is 115 degrees, that the both pairs of opposite angles are congruent. This is one where you could use either of those tests to prove that this is a parallelogram. But we'll stick with the consecutive angles one for this answer. Number eight also gives us information about diagonals. This is our diagonal test, but it doesn't necessarily show that the diagonals bisect each other. We don't know what these values are right here, even though it looks like they would be equal. Unless we're told the information, we cannot assume that something is going to be equal. And so this is going to be a no answer. So again, I want you to maybe pause the video, see if you can come up with a quadrilateral that meets this criteria where you have each of the half of diagonals that are three and four, but clearly not a parallelogram. My answer here is, again, another kite that the criteria, the given information, is the same, but this is clearly not a parallelogram. Number nine gives us information about opposite angles. We know that we have two sets of opposite angles that are congruent, and that is our number three test. We'll put that form of a conditional statement and say, yes, this is a parallelogram, because if both opposite angles are congruent, then it is a parallelogram. Then gives us information about angles also, but only these two angles. We don't know the value of these two. We can assume that they are 110 and 70, but unless we know for sure, we can draw a counter example that shows something else. So we do not have enough information, and I'm going to draw a pit that has the 110 and the 70, but clearly these other two angles do not create a parallelogram, and in fact, I could even add values for these other two angles. I don't need to do that, but let's just say this, 85 and 95, because then those four angles together will equal 360 that create any quadrilateral. But this clearly you could just draw the picture like this, and that would be enough information to show that no, this is not a parallelogram. Our picture gives us information about diagonals again. They tell us that SO is 8.