1. 5.4 Medians and Altitudes

2. Theorems

3. Centroid
The centroid is the point of concurrence for the medians of a triangle
It is a point that is 2/3 of the distance from each of the vertices
It is the center of gravity for a triangle, the triangle will balance at this point

4. Altitude
The altitude of a triangle is the perpendicular segment from the vertex to the opposite side

5. Orthocenter
The orthocenter is the point of concurrence of the altitudes of a triangle

6. Orthocenter on Acute, Obtuse, and Right Triangles
The red dot is the orthocenter

7. Uses of the Orthocenter
Unlike the Incenter, Circumcenter and Centroid, I can’t find any applications for the Orthocenter but it does some unusual things.

8. Uses ?

9. Odd Stuff

10. Homework examples