The orthocenter of a triangle may lie outside the triangle because the altitude does not necessairly intersect the?

My daughter's math teacher recommended the following site, which was enormously helpful for her. Here's a link to the 'orthocenter' topic, and you can find a bunch of other math topic videos there. It is all free. Hope it will help.

http://www.brightstorm.com/d/math/s/geometry/u/constructions/t/constructing-the-orthocenter