Assignment 8: Investigation of the Orthocenter

By: Moni Olubuyide

Given triangle ABC. Construct the Orthocenter H. Let points D, E, and F be the feet of the perpendiculars from A, B, and C respectfully. Prove:

1. (HD/AD) + (HE/BE) + (HF/CF) = 1

2. (AH/AD) + (BH/BE) + (CH/CF) = 2

To prove the first proof (HD/AD) + (HE/BE) + (HF/CF) = 1, will the examine the area of the color coded triangles below.

Now on to the second proof. In order to complete the proof we will also use the first proof.