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# Intro to rotational symmetry

CCSS.Math:

## 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 180 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 rotated 180 degrees so let me show you what that looks like we're going to rotate around its center 180 degrees 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 180 degrees and notice the figure looks exactly the same this one the square is unchanged by 180 degree rotation now what about this trapezoid right over here let's think about what happens when it's rotated by 180 degrees so that is 90 degrees and 180 degrees so this has now been changed now I have the short side or the show I have my basis short and my top is long before my base was long and my top was short so when I rotated 180 degrees I didn't get to the exact same figure I have essentially an upside down version of it so what I want to do for the rest of these is pause the video and think about which of these will be unchanged in which of them well will be changed when you rotate by 180 degrees so let's look at the star thing and one way that my brain visualizes it imagine the center that's what we're rotating around and then if you rotate 180 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 you rotate 180 degrees you go over here you go on 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 180 degrees it is unchanged now let's look at this parallelogram right over here so it's Center if we think about its center where my 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 distrophy were to go that same distance again you would get to that so it seems like that point would end up there that point would end up there and vice versa so I think this one will be unchanged by rotation so let's verify it so you go 90 degrees and then you go 180 degrees or I should say it will be unchanged by a rotation of 180 degrees around its center we got the same figure now let's think about this triangle so if you think about the center of the figure let's say the center of the figure is right around right around here if you take this point go to the center of the figure and then go that distance again you end up in a place where there's no point right now so that point is going to end up there this point is going to end up there this point is going to end up here so you're not going to have the same figure anymore and so we can rotate it to verify so that's rotated 90 degrees and then that's rotated 180 degrees so we've kind of turned this thing on its side it is not the same thing now let's think about this figure right over here well this figure if you rotate 180 degrees this point is now going to be down here and this point is going to be up here so you're going to make essentially is going to be an upside down version of the same kite and we can view that we can visualize that now so it's going to be different but let's just show it so that is 100 and this is 90 degrees and now this is 100 and 180 degrees if it if it was actually symmetric if it actually was symmetric about about the horizontal axis then we would have a different scenario we would have a different scenario with this thing right over here if it was some type of a parallelogram or a rhombus or something like that then this could have been more interesting but in this situation in this situation if it was just kind of a more symmetrical diamond shape than we would have then the trend this rotation would not have affected it but this one clearly did