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## High school geometry

### Unit 2: Lesson 4

Symmetry# Intro to reflective symmetry

CCSS.Math: ,

Introduction to the concept of an "axis of symmetry". Created by Sal Khan.

## 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.