Constructing Altitudes - Problem 2


In this problem we’re being asked to construct altitude BD, but what is an altitude? Well an altitude is a perpendicular segment from a vertex to the line containing the opposite side. Mr. McCall why don’t you just write that’s a perpendicular segment to the opposite side? Well the reason why is because when you have a problem like this where you have an obtuse triangle, you’re going to have to extend one side.

Since we’re starting at vertex B and we’re going perpendicular to AC, it’s going to fall somewhere in here. So what I’m going to do is I’m going to extend that side, and the reason why we have to do that is because otherwise we won’t have any room to see where our arc intersects AC.

So let’s start off by taking your compass and you’re going to swing an arc from point B so that it intersects this line right here. So I’m going to start off and I’m going to put a sharp end on point B and I’m going to swing my arc. Now the key thing is to make sure that both of these points are far apart. If they’re really close together, your construction won’t look too good.

So now we need to swing two more arcs from these two points compass stays the same for both of these so I’m going to swing one arc right there I’m going to swing another arc right there so we have our point of intersection and we have our vertex B, so that’s enough information to draw a line. And since it says line segment BD, I want to make sure that I’m drawing a line segment, I’m going to drop this down. I’m going to show that this is a 90 degree angle or a perpendicular segment and last I’m going to label that as point D. So remember in obtuse triangles, some of you altitudes will be outside of your triangle and that’s okay.

altitudes perpendicular segment vertex opposite side obtuse acute right triangles