Assignment #8: Altitudes and Orthocenters


Laura Singletary

Consider this Problem: Given triangle ABC. Construct the Othrocenter H. Let D, E, and F be the feet of the perpendiculars from A, B, and C respectfully. Prove the following:



It is important to notice that the triangle ABC used in this proof is not an obtuse triangle. We must consider - what might happen if the triangle was obtuse?

If the triangle is obtuse, where is the orthocenter located? Consider exploring this GSP file to determine why this ratios with the orthocenter and the altitudes do not exist when the triangle is an obtuse triangle.