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CCSS.Math: ,

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 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 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 just to go through the exercise so this point if you're reflected it across this blue line would get you here this point would in a different color this point if you were to reflect it across this blue line it would get you make sure I could do that it relatively straight I can do a straighter job than that so if you go about that distance about it and I'm going to go straight down into the blue line and say I'm gonna 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 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 it's mirror image of this top part would look something like this would look something something like 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 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 the is some type of a this is some type of a lake that 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