Orthocenter

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.