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# Intro to reflective symmetry

CCSS Math: HSG.CO.A.3

## Video transcript

For each of these diagrams, I want to think about whether this blue line represents an axis of symmetry. And the way we can tell is if on both sides of the blue line we essentially have mirror images. So let's imagine. Let's take this top part of this polygon, the part that is above this blue line here, and let's reflect it across the blue line-- you could almost imagine that it's a reflection over some type of a lake or something-- and see if we get exactly what we have below. Then this would be an axis of symmetry. So this point right over here, this distance to the blue line, let's go-- the same amount on the other side would get you right there. And so you immediately see we start ending up with a point that is off what's actually here in black, the actual bottom part of the polygon. So this is a pretty good clue that this is not an axis of symmetry. But let's just continue it, just to go through the exercise. So this point, if you reflected it across this blue line, would get you here. This point-- I'll do it in a different color. This point, if you were to reflect it across this blue line, it would get you-- let me make sure I can do that relatively straight. I can do a straighter job than that. So if you go about that distance about it, and I want to go straight down into the blue line, and I'm going to go the same distance on the other side, it gets me to right around there. And then this point over here, if I were to drop it straight down, then if I were to go the same distance on the other side, it gets me right around there. And then finally, this point gets me right around there. So its mirror image of this top part would look something like this. My best attempt to draw it would look something like this, which is very different than the part of the polygon that's actually on the other side of this blue line. So in this case, the blue line is not an axis of symmetry. So this is no. No, this blue line is not an axis of symmetry. Now let's look at it over here. And our eyes pick this out very naturally. Here you can see that it looks like this blue line really divides this polygon in half. It really does look like mirror images. It really does look like, if you imagine that this is some type of a lake, a still lake, so I shouldn't actually draw waves, but this is some type of a lake, that this is the reflection. And we can even go point by point here. So this point right over here is the same distance from, if we dropped a perpendicular to this point as this one right over here; this one over here, same distance, same distance as this point right over here; and we could do that for all of the points. So in this case, the blue line does represent an axis of symmetry.