Altitudes

2 videos
Ok. You knew triangles where cool, but you never imagined they were this cool! Well, this tutorial will take things even further. After perpendicular bisectors, angle bisector and medians, the only other thing (that I can think of) is a line that intersects a vertex and the opposite side (called an altitude). As we'll see, these are just as cool as the rest and, as you may have guessed, intersect at a unique point called the orthocenter (unbelievable!).

Proof: Triangle altitudes are concurrent (orthocenter)

VIDEO 10:01 minutes
Showing that any triangle can be the medial triangle for some larger triangle. Using this to show that the altitudes of a triangle are concurrent (at the orthocenter).

Common orthocenter and centroid

VIDEO 6:25 minutes
Showing that a triangle with the same point as the orthocenter and centroid is equilateral