 In this section, we're going to be discussing how we can know for sure that a certain shape is a parallelogram. Before we get to the actual test for parallelograms, let's take a look at this shape that looks like a parallelogram, but can I say for certain that it is a parallelogram? I can't say it is because we don't have enough information. I know it has four sides, so it's a quadrilateral, but because I don't have more specific information, I can't say for sure that it's a parallelogram. We're going to be doing with these tests for parallelograms. Each of these six tests are conditions that will ensure that a certain four-sided figure, we can say, is a parallelogram. So what I want you to do is draw a parallelogram and then just add the given information to that shape. So the first one says if both pairs of opposite sides are parallel, then it is a parallelogram. So if you're showing a figure now where we're showing that both sides, both pairs of opposite sides are parallel, then we can say yes, it is a parallelogram. So go ahead and draw a parallelogram and then add the symbols to show the opposite sides are parallel. And remember, you need to do one set of opposite sides with one arrow and the other set with two arrows to differentiate that. Our second test talks about opposite sides being congruent. And I actually have two parallelograms here because in one instance, we can just be given this information and that's enough to say if both pairs of opposite sides are congruent, then yes, this is a parallelogram. So we could just have the congruency marks or we could have more detailed information given to us that let's say we were given this. This also shows that opposite sides are congruent. So either one of those situations would say yes, that's a parallelogram. The next one, I also have two because when we're talking about opposite angles being congruent, again, we can just be shown the congruency marks and that right there is enough information to say if both pairs of opposite sides are congruent, then yes, it is a parallelogram. And again, if we didn't have the congruency marks, if we had detailed information about that side, we know that, or about those angles, we know that those opposite angles are congruent. So in either of these situations, if both pairs of opposite angles are congruent, then it is a parallelogram. Our next one talks about diagonals and again, we can show the diagonals. You can draw the diagonals in and I would need to see that those two pieces are congruent and then differentiating that the opposite sides of the other diagonals are also congruent. And just like the sides and the angles, we could also be given information more specific about the diagonals either with the congruency marks or with specific measures. In both of those cases, if diagonals bisect each other, then it is a parallelogram. This next one is one that isn't as common, I guess. A pair of opposite sides is both parallel and congruent. This is the key information here that we're just talking about one set of opposite sides. So if we know that these two sides are parallel and at the same time that same side is also congruent, then we can say that it is a parallelogram. Keep in mind it has to be the same side. Sometimes you'll see this situation where we have this set of sides parallel and the other set of sides congruent and this is not enough information to say it's a parallelogram. So this would be not a parallelogram. This one, both parallel and congruent on the same side. Consecutive angles are supplementary is our last one. And remember we know consecutive angles are any set of angles that are next to each other or adjacent. So these would be consecutive angles. These would be consecutive angles. We have four sets of consecutive angles in any quadrilateral. And when we say consecutive angles are supplementary, we just have to be given information if we were told that this was true. We know that one set of consecutive angles is supplementary, but we need to know that all of them are supplementary. So now I have all four sets of consecutive angles supplementary. Additionally, these also would pass the test for the third one. So consecutive angles are congruent because these are opposite angles. But you'll see in our next example videos that they specifically are going to talk about consecutive angles being supplementary. So if you have a quadrilateral and any of these six things are true, then you can say yes it is a parallelogram.