Identifying bases and heights of parallelograms

0:00- [Narrator] So I have two parallelograms here and we've labeled the base of each of these parallelograms. The base they're saying is the side that I am recoloring in as red. And what I want you to do is pause this video and see if you can figure out what the height of each of these parallelograms are.

0:18All right, now let's do this together. So the height of a parallelogram, it's going to be perpendicular to the base. What does that mean? That means a right angle or a 90-degree angle. So for example, if that's the base, if I have a right angle to this, this base is straight horizontal.

0:37So a right angle to that would be directly vertical. And we're essentially going from this base to the top of the parallelogram. And actually you could even consider that another base. You could imagine flipping this parallelogram over. But when you go from one base to another base like this at a right angle to either of those bases, this is also a right angle here.

1:00Then you have the height. So the height in this situation is one, two, three units, three units, and that is the height. Let's do another example right over here. Now this one is interesting because if I were to just do the same thing, if I were to just start right over here and go perpendicular to it, I need to go outside of the parallelogram to get to the same height where you could say the other, the opposite side to that base.

1:31You could even consider that to be another base to see where that is. But if you do that, that indeed is the height. So notice this is parallel. This is perpendicular to both of those bases, even though it went outside. And you can see that it is one, two, three, four, five, six units, six units.

1:50Sometimes you might see it like this where you could start over here and you could go one, two, three, four, five, six. The key is is that you're looking at this base or that base and you are just seeing the height between the two. And you might even think about extending them like that and taking a perpendicular line, a 90-degree angle to see how far it is.

2:17Now we've gotten a little bit of practice, given the base, what could be the height? Let's go the other way around. Given the height, what could be the base? So in this situation, let's say that this length here, E in the dotted line, let's say that that is the height.

2:35So given that, which of these sides could be the base? Well, you would use the same logic we've just talked about. The height is going to be perpendicular to the bases, is one way to think about it. And we see it already labeled, we have a 90-degree angle right over here.

2:53And so side C can be a base, but so could side A, this is a parallelogram. Side A is parallel to side C. So if you're perpendicular to side C, you're also going to be perpendicular to side A. So side A can also be a base, just as I said, this could be a base or that could be a base.

3:16This could be a base or that could be a base for these heights. Similarly, this could be a base, sorry. Similarly for this height, A or C could be bases and we're done.