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# Constructing the Orthocenter - Concept

###### Brian McCall

###### Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

The orthocenter is the point of concurrency of the altitudes in a triangle. A point of concurrency is the intersection of 3 or more lines, rays, segments or planes. The **orthocenter** is just one point of concurrency in a triangle. The others are the incenter, the circumcenter and the centroid.

One of the four main points of concurrency

of a triangle is the orthocenter.

The orthocenter is where the

three altitudes intersect.

If we look at three different types of triangles,

if I look at an acute triangle

and I drew in one of the altitudes or

if I dropped an altitude as some

might say, if I drew in another altitude,

then this point right here will

be the orthocenter.

I could also draw in the third altitude,

but I know that since this is a point

of concurrency the three altitudes must

intersect there so I only have

to draw two.

If we look at a right triangle, if I were

to draw in an altitude from that vertex,

well, that just happens to be this

leg of this right triangle.

If I drew in the altitude of this triangle,

then I would see -- excuse me, this

side, then this leg would

be its altitude.

And if we drew in this last one from our

90-degree angle, we see that the point

where they are concurrent is right

at the vertex of that right angle.

So in a right triangle your orthocenter

will be at the vertex of the right

angle.

And, last, if we look another an obtuse

triangle, we remember in order to find

the altitude of this side we have to extend

that side drop down an altitude

which is outside of our triangle to find

-- and I'm just going to extend

this -- to find the ortho -- to find

the altitude from this vertex, I'm

going to draw a perpendicular

segment through the vertex.

So it looks like it's going to intersect

right over there, and for this third

side I would have to extend it until

we could find our 90-degree angle.

Okay.

So in an obtuse triangle your orthocenter

will be outside of your triangle.

So expect that on a quiz.

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###### Brian McCall

B.S. in Chemical Engineering, University of Wisconsin

J.D. University of Wisconsin Law School (magna cum laude)

He doesn't beat around the bush. His straightforward teaching style is effective and his subtle midwestern accent is engaging. There's never a dull moment with him.

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