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CCSS.Math:

which shapes are symmetrical to answer this we need to know what it means for a shape to be symmetrical a shape is symmetrical if it has at least one line of symmetry a line of symmetry and now that answer is only helpful if we know what a line of symmetry is so let's talk about it a line of symmetry is a line where we can fold the image and have both halves match exactly let's look at an example let's draw let's going to draw a circle and then we can put a line on that circle let's draw a line maybe somewhere like this this line is a line of symmetry if we can take one side of the line and fold it on to the other and have them match exactly so let's take one side doesn't matter which one let's say the top the top side and if we were going to fold this top side down on to the bottom would it match exactly what is shown under here let's see it would probably look something like this and does that match exactly no definitely not so this is not a line of symmetry let's try another line maybe if we drew a line and we'll try to get as close down the center as we can here like this try to be as close to center as possible and here if we took one side again it doesn't matter which side let's say over here let's say the left side and we folded this left side on to the right side would it match exactly and if our line truly was in the center of the circle then yes it would which means that this line is a line of symmetry and because we can draw this line of symmetry on our circle it means that our circle is symmetrical shapes are symmetrical if they have at least one line of symmetry and circles have many many many lines of symmetry there was many places we could have drawn a line and folded it so that it worked so the two halves matched exactly but here's one and as soon as we find one we know we have a symmetrical shape so let's go back to the shapes we were given we can start with the triangle if we draw a line maybe a vertical line let's try to draw it as close to the middle as possible something like this and we fold let's take one side if we fold this side over these two lines might match up nicely but this line here is going to create something more like this which does not match which is what's shown over here so that's not a line of symmetry and anywhere else vertical same thing we're not going to have it lined up so let's try maybe a horizontal line is there anywhere horizontally we could draw a line and again I think we're going to see the same thing at the top and the bottom of the line are not going to match up exactly so maybe one last thing we could try as a diagonal line something like this maybe this could be our line of symmetry if we fold this bottom side this might line up pretty nice here and then this side is going to do something like this so it's close it's the closest we've gotten but still does not match exactly for it to be a line of symmetry it needs to match exactly so we weren't able to find a way to draw a vertical line or a horizontal line or even the diagonal line so this shape has no lines of symmetry so we can say it is not symmetrical moving on to the rectangle let's try here again this time we will try a horizontal line we can draw one right here and if that line truly is in the middle which is what I've tried for then this side should match up nicely to this one across the top should match across the bottom and these sides if I was right at the halfway point should fold over each other also so it has a line of symmetry so it is symmetrical it has more than one line cemetry it has another one in the middle right here but once we found one we know that it's symmetrical and finally let's look we have a Pentagon here again try and align in the middle in some way is usually a good way place to start we can try to draw a line right if this is right down the center here then if we folded this side should line up nicely to this side this side and this side would overlap and these two would match exactly so again has one line of symmetry so it is symmetrical and just like the rectangle this one had quite a few lines of symmetry here's another line of symmetry here's another line of symmetry here's one more line of symmetry and so it has quite a few it has it looks like one two three four lines of symmetry but as long as it has one it is symmetrical so of the shapes we were given the rectangle and the Pentagon were symmetrical