Current timeTotal duration Google Classroom Facebook Twitter. Video transcript We have two copies of six different figures right over here. And I want to think about which of these figures are going to be unchanged if I were to rotate it degrees? So let's do two examples of that. So I have two copies of this square. If I were to take one of these copies and rotate it degrees.
So let me show you what that looks like. And we're going to rotate around its center degrees. So we're going to rotate around the center. So this is it. So we're rotating it. That's rotated 90 degrees. And then we've rotated degrees. And notice the figure looks exactly the same. This one, the square is unchanged by a degree rotation. Now what about this trapezoid right over here? Let's think about what happens when it's rotated by degrees. So that is 90 degrees and degrees.
So this has now been changed. Now I have the short side. I have my base is short and my top is long. Before my base was long and my top was short. So when I rotate it degrees I didn't get to the exact same figure. I have essentially an upside down version of it. So what I want you to do for the rest of these, is pause the video and think about which of these will be unchanged and which of them will be changed when you rotate by degrees. So let's look at this star thing. And one way that my brain visualizes it, is imagine the center.
That's what we're rotating around. And then if you rotate degrees. Imagine any point. Say this point, relative to the center. If you were to rotate it 90 degrees, you would get over here. And then if rotate it degrees, you go over here. You go the opposite side of the center from where it is. So from that point, to the center, you keep going that same distance. You'll end up right over there. So this one looks like it won't be changed.
But let's verify it. So we're going to rotate 90 degrees. And then we have degrees. It is unchanged. Now let's look at this parallelogram right over here. So its center, if we think about its center where my cursor is right now-- Think about this point. The distance between that point and the center, if we were to keep going that same distance again, you would get to that point. Likewise, the distance between this point and the center, if we were to go that same distance again, you would to get to that point.
So it seems like that point would end up there. That point would end up there. Well since they are 6 congruent angles we're going to have to do divided by 6. Well divide by 6 is 60 degrees so this figure right there has 60 degrees of rotational symmetry. Last we look at this plus sign. If I had drawn this perfectly it's pretty clear that after, that there are 4 ways that we can rotate this so if we take degrees and we rotate it 4 different ways it's pretty clear that this will have 90 degrees of rotational symmetry.
So again rotational symmetry what does it mean? It means that you can rotate it less than degrees and the figure will be exactly the same and if you can rotate it exactly degrees so let's say we had a figure kind of like this, you see that if I rotate it exactly degrees it would be itself. All Geometry videos Unit Transformations. Previous Unit Circles. Next Unit Area. Brian McCall.
Thank you for watching the video. Start Your Free Trial Learn more. Brian McCall Univ. Explanation Transcript Symmetry in a figure exists if there is a reflection , rotation , or translation that can be performed and the image is identical. Geometry Transformations.
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