If I look at the other two altitudes in this obtuse triangles, we're going to have one altitude going like that I'm going to have to extend that side as well and we'll drop down another altitude. Notice that I had to extend that opposite side. So if we pick this vertex, our opposite sides are over here but that opposite side doesn't continue to where this altitude will drop. So a third case is the obtuse triangle, and here is where I say to a line containing the opposite side. However if I pick my 90 degree angle as my vertex, then we'll be able to see that altitude inside the triangle. If I pick this vertex right here the altitude will just be that leg of the triangle. That's going to be that leg of the triangle. If we look at a right triangle over here we can see that if I pick this vertex right here, we already have an altitude drawn. Notice that all three altitudes are inside the triangle. We would have two more altitudes, each of which would go perpendicular to the opposite side.
So if I were to pick this top vertex right here, the altitude would go straight down perpendicular to the opposite side. So if we look at an acute triangle, there are going to be three altitudes, one form each vertex. It's not always to the opposite side and you're going to see why in a second here. So this definition is written very carefully. Altitude of a geometric figure is the shortest distance plete information about the altitude, definition of an altitude, examples of an altitude, step by step solution of problems involving altitude. What we're talking about is a perpendicular segment, remember this symbol right here means perpendicular-I'm trying to get you used to seeing these symbols-from a vertex to a line containing the opposite side. When we're talking about triangles, there's a special segment three in each triangle called an "Altitude." So we're not talking about skiing here.
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