Euler Line

Review of Triangle Properties
Euler Line
Euler's Line Proof

Euler Line The magic and mystery of the Euler Line

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Euler Line

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So I've drawn an arbitrary triangle,
That we will assume is an equilateral triangle,
And let's draw some of the interesting properties of this triangle.
Let's start with the perpendicular bisectors.
Let's say this is the midpoint of the side over here.
So this length is equal to this length right over here.
And so let me draw the perpendicular bisector.
Now the perpendicular bisector would look something like that.
Now let me do it on this side.
Just trying to eyeball it...
So this length is going to be equal to this length.
And then, once again, let me draw the perpendicular bisector.
So, its going to go at a 90 degree angle.
That looks pretty good...
And it is perpendicular.
Then, imagine what I will do with this side!
That looks like the midpoint.
This length is going to be equal to that length right over there.
And then if we draw a perpendicular,
My best attempt to draw this,
It looks something like that,
And we've already learned that these three lines
are going to intersect at a unique point,
right over there, which we call the circumcenter.
So this is our circumcenter.
This is nothing new.
Now lets draw the medians.
The medians go from each of the vertices to the,
to the opposite side.
So let me draw,
so this is a median,
This is a median,
This is a median,
And then this is...
and all the errors in my drawing will start to become apparent.
But I'm trying to do multiple things with it.
We know all of the medians intersect at the centroid.

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Euler Line The magic and mystery of the Euler Line

Euler Line

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